
	Where results make sense

Topic: Transcendence degree

	The transcendence degree of the mod p cohomology of finite Postnikov systems (Site not responding. Last check: 2007-10-21)
		Abstract: We examine the transcendence degree of the mod p cohomology of a finite Postnikov system E. We prove that, under mild assumptions on E, the transcendence degree of H(E;F_p) is always positive, and give a complete classification of the Postnikov systems where the transcendence* degree of H*(E;F_p) is finite.
		More precisely we prove that H(E;F_p) is of finite transcendence* degree iff E is F_p-equivalent to the classifying space of a p-toral group.
		To obtain the results we establish a general formula for determining the transcendence degree of an unstable algebra given in terms of the growth of certain 'unstable Betti numbers'.
	www-math.mit.edu /~jg/papers/postnikov.html (213 words)

	Springer Online Reference Works
		(that is, a finitely generated field extension of transcendence degree at least one; cf.
		Since there is no hope for a general classification of valued function fields up to isomorphism, it makes sense to pass to their Henselizations and use the universal property of Henselizations (see Henselization of a valued field).
		1) In the case of valued function fields without transcendence defect, natural criteria can be given for the isomorphism class of their Henselizations to be determined by the isomorphism classes of the value group and the residue field.
	eom.springer.de /V/v110010.htm (1083 words)

	Galois Theory Glossary
		An element a of a field L is algebraic of degree n over a subfield K if there is an irreducible polynomial f(t) in K[t] of degree n such that f(a) = 0.
		The degree [L:K] of an extension L/K is the dimension of L as a vector space over K. The multiplication formula for degrees asserts that given extensions M/L, L/K then [M:K] = [M:L][L:K].
		The transcendence degree of an extension L/K is the maximum number of elements of L that are algebraically independent over K.
	www.wra1th.plus.com /Galois/gloss.html (892 words)

	Belford University - Life Experience Degrees
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	www.belforduniversity.org (274 words)

	[No title]
		Here we define the transcendence degree, d(K), as the maximal number of homo- geneous algebraically independent elements in K. When K is noetherian, d(K) is equal to the Krull dimension of K. Note that Theorem 1.1 can be reformulated as saying that the transcendence degree of H*(E; Fp) is always positive.
		Note that the formula for the transcendence degree of H(E) in- volves the behavior of a certain class in the integral cohomology of P when res *trict- ing to elementary abelian subgroups.
		Then the transcendence degr* ee of H(E) is finite iff E is Fp-equivalent to a space E0 fitting into a principa* *l fibra- tion sequence of the form: CP1 x.
	hopf.math.purdue.edu /Grodal/postnikov.txt (6592 words)

	My Research Interests
		The behavior of transcendence degree is well known over an integral domain.
		It was a wonderful treat to only teach one course and pursue the issue of what transcendence degree properties could be generalized.
		I found enough bad examples to illustrate why one usually doesn't speak of transcendence degree outside of the domain case, but enough good results to feel I had exhausted the subject.
	www.math.sjsu.edu /~hamann/My_Research_Interests.html (982 words)

	Gerotranscendence - A Theoretical and Empirical Exploration
		The question of gerotranscendence and life satisfaction builds on the theory's assumption that the development toward gerotranscendence is a natural developmental process, which is followed by an increase in satisfaction.
		The higher the degree of transcendence, the higher the life satisfaction.
		When the respondents who have experienced such a loss are compared with the ones who have not, we find the degree of transcendence to be higher among those who have experienced that loss.
	www.soc.uu.se /research/gerontology/gero1.html (603 words)

	VITA (Site not responding. Last check: 2007-10-21)
		"Semiflat algebras and transcendence degree," J. Algebra., Vol.
		"Krull dimension and transcendence degree," Communications in Algebra, 18(4) (1990), 1189-1198.
		"Some transcendence degree questions," Proceedings of Microprogram on Commutative Algebra held June 15 - July 2, 1987, Mathematics Science Research Institute (MSRI), Springer Verlag, 1989.
	www.math.sjsu.edu /~hamann/hamannshort.html (104 words)

	Spirituality for Today April 2002
		It means to rise above, to transcend, to excel, to surpass.
		Does it ever occur to you to think that God wants you to transcend your daily life to excel and surpass so that the achievement you reach leaves the world a better place and your church a better place.
		The kingdom of heaven is filled with people who have lived out their lives aware of the value of transcendence.
	www.spirituality.org /is/081/page01.asp (1045 words)

	Transcendence (Site not responding. Last check: 2007-10-21)
		Transcendence expands the scope of the Monte Cook's Arcana Evolved variant player’s handbook, offering an array of new character options, abilities, and paths of evolution.
		Customize your character to a greater degree than ever before, or swear allegiance to the dragons and transcend the bounds of flesh and mind.
		Transcendence, the first rules expansion to Arcana Evolved, broadens the scope of options available to players and DMs.
	www.montecook.com /cgi-bin/page.cgi?mpress_Trans (769 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Abstract: Transcendence problems over function fields in characteristic p begin with periods of Drinfeld modules and go back to work of Carlitz and Wade in the 1930's and 1940's.
		Until recently theorems on transcendence and algebraic independence in characteristic p have mirrored what is known for their classical counterparts (even if their proofs were quite different!).
		More precisely, we show that the transcendence degree of the period matrix of a Drinfeld module is equal to the dimension of its Galois group.
	www.math.rice.edu /~hassett/seminar/papanikolas2.html (161 words)

	Ian Johnson's neurodiversity blog
		God is transcendent, Jesus transcended death, and, at some day in the future (at least for the fundamentalists and evangelicals)all believers will also experience transcendence.
		But anyone who claims to have experienced any degree of transcendence now, these same branches of Christianity insist, is either deluded, or mentally ill, or demonized.
		He assumes that "reality" really is as harsh as it seems, that there really is no transcendent reality behind it, and, therefore, any transcendent feelings we may have will, by definition, be false (i.e., not congruent with "primary reality").
	www.angelfire.com /weird2/ian_j_site2/index.blog?end=1141478197 (3938 words)

	Math Forum Discussions (Site not responding. Last check: 2007-10-21)
		> >the degree of a divisor D is defined as deg(D) = sum_{P} v_P(D).deg(P) > >where P is a point of a curve, or a place of the function field of the
		> The transcendence degree of that extension is always equal to 0
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /kb/thread.jspa?messageID=3412663&tstart=0 (360 words)

	Springer Online Reference Works
		, and is called the degree of the algebraic function.
		Such expansions of elements by fractional degrees of the difference
		The Riemann surface of a complete algebraic function is compact and is a
	eom.springer.de /A/a011490.htm (1619 words)

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	OUP: UK General Catalogue (Site not responding. Last check: 2007-10-21)
		Accordingly, the theory of affine algebras is featured, treated both directly and via the theory of Noetherian and Artinian modules, and the theory of graded algebras is included to provide the foundation for projective varieties.
		Major topics include the theory of modules over a principal ideal domain, and its applications to matrix theory (including the Jordan decomposition), the Galois theory of field extensions, transcendence degree, the prime spectrum of an algebra, localization, and the classical theory of Noetherian and Artinian rings.
		Transcendence degree and the Krull dimension of a ring
	www.oup.com /uk/catalogue/?ci=9780821805701 (382 words)

	Yekutieli's talk
		Let D be a finitely generated division algebra over a field K. In this talk I will present a new invariant of D called the homological transcendence degree.
		As the name suggests the definition involves homological algebra; but it is a very easy definition.
		a field extension of K) then this number coincides with the classical transcendence degree.
	www.math.bgu.ac.il /~bessera/seminar/13April05 (115 words)

	14a
		We generalize the notion of hypersurfaces of low degree to rationally connected varieties over
		There is another candidate for a generalization of hypersurfaces of low degree: a variety
		This is completely ineffective; an open question is to find the genus of the curve given by this counterexample.
	www.aimath.org /WWN/qptsurface2/articles/html/14a (474 words)

	Message Update 2006 (Site not responding. Last check: 2007-10-21)
		Our sensitive relationship with all creatures, including humanity as well as other dimensional life forms, can never be without a certain degree of transcendence of the self.
		This is not a ‘make believe’ transcendence of our space and time, but that which brings forth the true gifts of Life.
		Spiritual wisdom gives us the capacity to rise above personal suffering while we continue to care and have concern for our brothers and sisters.
	www.keysofenoch.org /html/message_update_2006.html (654 words)

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