
	Where results make sense

Topic: First isomorphism theorem

Related Topics

First World War

First ascent

first person shooter

First Lady of the United States

First Nations

First Lord of the Admiralty

First Age

First Amendment

first past the post

First Crusade

First Ladies

First past the post electoral system

In the News (Fri 27 Nov 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Kids.Net.Au - Encyclopedia > Isomorphism theorem
		In mathematics, the isomorphism theorems are 3 theorems that apply broadly in the realm of universal algebra.
		First we state the isomorphism theorems for groups, where they take a simpler form and state important properties of factor groups (also called quotient groups).
		The isomorphism theorems are also valid for modules over a fixed ring R (and therefore also for vector spaces over a fixed field).
	www.kids.net.au /encyclopedia-wiki/is/Isomorphism_theorem (317 words)

	Kernel (algebra) - Wikipedia, the free encyclopedia
		The first isomorphism theorem for vector spaces states that this quotient space is naturally isomorphic to the image of T (which is a subspace of W).
		The first isomorphism theorem for monoids states that this quotient monoid is naturally isomorphic to the image of f (which is a submonoid of N).
		The first isomorphism theorem in general universal algebra states that this quotient algebra is naturally isomorphic to the image of f (which is a subalgebra of B).
	en.wikipedia.org /wiki/Kernel_(algebra) (1892 words)

	Isomorphism theorem
		In mathematics, the isomorphism theorems are 3 theorems that apply broadly in the realm of universal algebra.
		First we state the isomorphism theorems for groups, where they take a simpler form and state important properties of factor groups (also called quotient groups).
		The isomorphism theorems are also valid for modules over a fixed ring R (and therefore also for vector spaces over a fixed field).
	www.ebroadcast.com.au /lookup/encyclopedia/no/Noether_isomorphism_theorem.html (312 words)

	PlanetMath: proof of third isomorphism theorem
		We'll give a proof of the third isomorphism theorem using the Fundamental homomorphism theorem.
		Cross-references: first isomorphism theorem, kernel, surjective, homomorphism, subset, natural homomorphisms, normal subgroups, group, fundamental homomorphism theorem, third isomorphism theorem
		This is version 2 of proof of third isomorphism theorem, born on 2005-11-22, modified 2006-10-10.
	www.planetmath.org /encyclopedia/ProofOfThirdIsomorphismTheorem.html (85 words)

	:::► Dictionary of Meaning www.dictionary-of-meaning.com ◄:::
		The first isomorphism theorem for vector spaces states that this quotient space is naturally isomorphic to the image (function) of T (which is a subspace of W).
		The first isomorphism theorem for monoids states that this quotient monoid is naturally isomorphic to the image (function) of f (which is a image (function) of f (which is a submonoid of N).
		The first isomorphism theorem in general universal algebra states that this quotient algebra is naturally isomorphic to the image (function) of f (which is a image (function) of f (which is a subalgebra of B).
	www.dictionary-of-meaning.com /kernel_(algebra).html (2117 words)

	Isomorphism theorem - Wikipedia, the free encyclopedia
		In mathematics, the isomorphism theorems are three theorems, applied widely in the realm of universal algebra, stating the existence of certain natural isomorphisms.
		If G and H are groups and f is a homomorphism from G to H, then the kernel K of f is a normal subgroup of G, and the quotient group G/K is isomorphic to the image of f.
		Let H and K be subgroups of the group G, and assume H is a subgroup of the normalizer of K.
	en.wikipedia.org /wiki/Isomorphism_theorem (334 words)

	PlanetMath: proof of second isomorphism theorem for groups
		"proof of second isomorphism theorem for groups" is owned by yark.
		Cross-references: isomorphism, canonical, first isomorphism theorem, homomorphism, surjective, intersection, closed under inverses, multiplication, closed under, normal subgroup, subgroup
		This is version 13 of proof of second isomorphism theorem for groups, born on 2002-07-02, modified 2007-05-23.
	planetmath.org /encyclopedia/ProofOfSecondIsomorphismTheorem.html (119 words)

	PlanetMath: proof of fundamental theorem of Galois theory
		The theorem is a consequence of the following lemmas, roughly corresponding to the various assertions in the theorem.
		Cross-references: first isomorphism theorem, kernel, primitive element theorem, automorphism, surjective, implication, map, separable extension, homomorphism, implies, fixed, equality, normal subgroup, the following are equivalent, quotient groups, properties, fixed field, inverse, bijection, function, clear, roots, divides, minimal polynomial, polynomial, splitting field, separable, normal, contained, extension fields, subgroups, Galois group, fields, Galois extension, finite-dimensional
		This is version 2 of proof of fundamental theorem of Galois theory, born on 2004-06-23, modified 2004-06-29.
	planetmath.org /encyclopedia/ProofOfFundamentalTheoremOfGaloisTheory.html (297 words)

	Kernel of a function - Wikipedia, the free encyclopedia
		The coimage is naturally isomorphic (in the set-theoretic sense of a bijection) to the image, im f; specifically, the equivalence class of x in X (which is an element of coim f) corresponds to f(x) in Y (which is an element of im f).
		First, if X and Y are algebraic structures of some fixed type (such as groups, rings, or vector spaces), and if the function f from X to Y is a homomorphism, then ker f will be a subalgebra of the direct product X × X.
		Thus the coimage of f is a quotient algebra of X much as the image of f is a subalgebra of Y; and the bijection between them becomes an isomorphism in the algebraic sense as well (this is the most general form of the first isomorphism theorem in algebra).
	en.wikipedia.org /wiki/Kernel_of_a_function (511 words)

	Section (vi) The First Isomorphism Theorem as a Container of Compressed Conceptual Group-Theoretical Obstacles
		Patricia's association with 'division' (possibly invoked by the use of '/' in the statement of the theorem) is accompanied by her query on the meaning of ~.
		In sum, retrieval of the theorem is generally problematic.
		Cleo's antonyms (it) as the subject of the verb 'maps' (C1 and C3) as well as her substituting the verbs (C4 and C5) with 'does' are lexical substitutions that possibly reflect and determine the ambiguity of her thinking.
	www.uea.ac.uk /~m011/thesis/chapter9/9vi.htm (1436 words)

	PlanetMath: proof of first isomorphism theorem
		and show that it is a function, a homomorphism and finally an isomorphism.
		"proof of first isomorphism theorem" is owned by uriw.
		This is version 6 of proof of first isomorphism theorem, born on 2002-05-21, modified 2004-04-12.
	www.planetmath.org /encyclopedia/ProofOfFirstIsomorphismTheorem.html (122 words)

	Isomorphism theorem - Definition, explanation
		In mathematics, the isomorphism theorems are three theorems, applied widely in the realm of universal algebra, stating the existence of certain natural isomorphisms.
		Let H and K be subgroups of the group G, and assume H is a subgroup of the normalizer of K.
		The isomorphism theorems are also valid for rings, ring homomorphisms and idealss.
	www.calsky.com /lexikon/en/txt/i/is/isomorphism_theorem.php (340 words)

	Isomorphism theorem -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-05)
		First we state the isomorphism theorems for ((chemistry) two or more atoms bound together as a single unit and forming part of a molecule) groups, where they take a simpler form and state important properties of (Click link for more info and facts about quotient group) quotient groups (also called factor groups).
		Let H and K be subgroups of the group G, and assume H is a subgroup of the (A person who normalizes) normalizer of K.
		The isomorphism theorems are also valid for rings, ring homomorphisms and (The idea of something that is perfect; something that one hopes to attain) ideals.
	www.absoluteastronomy.com /encyclopedia/i/is/isomorphism_theorem.htm (327 words)

	Joel Cohen (Site not responding. Last check: 2007-11-05)
		THEOREM: A set whose only element is a set may be isomorphic to a set whose only element is a set whose only elements are a subgroup of the group of elements in the set which is the only element of the set with which it is isomorphic (sick).
		First, we note the obvious fact that historians always tell the truth (for historians always take a stand, and, therefore, they cannot lie).
		The first is the famous Goldbrick conjecture from the theory of numbers, which states that every prime number is expressible as the sum of two even numbers.
	pages.ripco.net /~marnow/cohen (1678 words)

	An Introduction to Banach Space Theory
		The first section includes some topological preliminaries, but is devoted primarily to a fairly extensive development of the theory of nets, including characterizations of topological properties in terms of the accumulation and convergence of certain nets.
		Schauder's theorem relating the compactness of a bounded linear operator to that of its adjoint is presented, as is the characterization of operator compactness in terms of the bounded-weak*-to-norm continuity of the adjoint.
		Gantmacher's theorem is obtained, as well as the equivalence of the weak compactness of a bounded linear operator to the weak*-to-weak continuity of its adjoint.
	www.math.lsa.umich.edu /~meggin/ibst.html (2875 words)

	MTH 619: Course Schedule
		Cosets and normal subgroups; quotient groups (1.3); the first isomorphism theorem; classification of cyclic groups (1.4); free groups (1.12).
		Ring homomorphisms; ideals; principal ideals and principal ideal domains; quotient rings; the first isomorphism theorem for rings; characteristics of rings and prime fields, prime ideals and maximal ideals; irreducible elements in rings.
		Roots of polynomials; Eisenstein irreducibility criterion; the fundamental theorem of algebra.
	www.math.buffalo.edu /~badzioch/mth619/schedule.html (307 words)

	The Isomorphism Theorems in Group Theory (Site not responding. Last check: 2007-11-05)
		The set of elements of G that map into the identity of H is called the kernel of the homomorphism and is denoted as Ker f.
		The kernel of a homomorphis is a normal subgroup of G. An isomorphism is a homomorphism with an inverse; i.e., a one-to-one correspondence that preserves the group relation ships.
		First Isomorphism Theorem: If f:G→H is an isomorphism then there is an isomorphism between the factor group of G with respect to its normal subgroup Ker f (G/(Ker f)) and the image of G under f in H, im f.
	www.applet-magic.com /isomorphism.htm (198 words)

	Correspondence Theorems (Site not responding. Last check: 2007-11-05)
		The correspondence theorem, or isomorphism theorem, is sometimes presented as three separate theorems.
		This theorem, or theorems if you prefer, asserts the equivalence of the subgroups or normal subgroups of G with those in the factor group H. In other words, subgroups containing K, or normal subgroups containing K, correspond 1-1 with subgroups or normal subgroups in the factor group G/K. Let's get started.
		Let K be a normal subgroup of G, with factor group H. If R is a subgroup of G, its image S is a subgroup of H. Conversely, if S is a subgroup of H, its preimage R is a subgroup of G. Use the a/b criterion to verify this.
	www.mathreference.com /grp,cor.html (350 words)

	Isomorphism theorem - Encyclopedia, History, Geography and Biography
		Then the join HK of H and K is a subgroup of G, K is a normal subgroup of HK, H ∩K is a normal subgroup of H, and HK/K is isomorphic to H/(H ∩K).
		The notation for the join in both these cases is "H + K" instead of "HK".
		Isomorphism theorem, Groups, First isomorphism theorem, Second isomorphism theorem, Third isomorphism theorem, Rings and modules and General.
	www.arikah.net /encyclopedia/Isomorphism_theorem (409 words)

	The isomorphism theorems
		The first isomorphism theorem tells us that the factor groups of G over its various normal subgroups are, up to isomorphism, precisely the homomorphic images of G.
		This is an important theorem that is self evident.
		The statement on normality follows from the third isomorphism theorem.
	www.pitt.edu /~gmc/ch1/node2.html (171 words)

	PlanetMath: first isomorphism theorem
		has the additional property mentioned in the statement of the theorem.
		Cross-references: function symbol, constant symbol, injective, homomorphic image, isomorphism, relation symbol, property, bimorphism, homomorphism, structures, signature, fixed
		This is version 6 of first isomorphism theorem, born on 2003-08-13, modified 2004-02-28.
	www.planetmath.org /encyclopedia/FirstIsomorophismTheorem.html (82 words)

	Peter Suber, "Glossary of First-Order Logic"
		A wff that is neither a theorem nor the negation of a theorem.
		The theorem implies that consistent first-order theories, including those intended to capture the real numbers or other uncountable sets, will be non-categorical; hence it implies that there is no consistent, categorical description of the reals in a first-order theory.
		Roughly, in the basis the theorem is proved to hold for the "ancestor" case, and in the induction step it is proved to hold for all "descendant" cases.
	www.earlham.edu /~peters/courses/logsys/glossary.htm (9715 words)

	MTH-2A23 : Algebra I (Site not responding. Last check: 2007-11-05)
		Lagrange's Theorem, saying that the order of a subgroup of a finite group divides the order of the group, is proved by showing that cosets partition the group.
		One of the most useful theorems on group actions is the Orbit Stabilizer Theorem, which will be used to count orbits and patterns.
		With the theory developed so far it is possible to classify all commutative groups generated by a finite number of elements and this result is one of the principal results in the course.
	www.mth.uea.ac.uk /maths/syllabuses/0001/2A2300.html (493 words)

	Isomorphism theorem : Noether isomorphism theorem
		All is still licensed under the GNU FDL.
		He considers it a fallacy to say that anything is him.
		The next thing to be done is to seek representatives of the great.
	www.termsdefined.net /no/noether-isomorphism-theorem.html (462 words)

Try your search on: Qwika (all wikis)