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Topic: Direct summand

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Injective module

Associative rings

Kernel of a homomorphism

	Direct sum -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		The (The magnitude of something in a particular direction (especially length or width or height)) dimension of V ⊕ W is equal to the sum of the dimensions of V and W.
		The direct sum can also be defined for abelian groups and for modules over arbitrary (Gymnastic apparatus consisting of a pair of heavy metal circles (usually covered with leather) suspended by ropes; used for gymnastic exercises) rings.
		The direct sum of these modules is then defined to be the set of all (A mathematical relation such that each element of one set is associated with at least one element of another set) functions α with domain I such that α(i) ∈ M
	www.absoluteastronomy.com /encyclopedia/d/di/direct_sum.htm (1391 words)

	PlanetMath: (Site not responding. Last check: 2007-10-08)
		direct sum (=categorical direct sum) owned by djao
		direct sum of even/odd functions (example) owned by mathcam
		direct sum of groups (in direct product and restricted direct product of groups) owned by yark
	planetmath.org /encyclopedia/D (1510 words)

	Abstracts
		These models are investigated within the context of PCCS, a dialect of Milner's SCCS in which each summand of a process summation expression is guarded by a probability and the sum of these probabilities is 1.
		We give a presentation of equational logic, infinitary conditional equational logic - of which we also proof the completeness - and first order logic and show how the notion of a formal proof of a formula from a theory can be generalized to that of a proof of a formula from a module.
		It is also argued that the use of the completeness result for branching congruence in obtaining the completeness result for weak congruence leads to a considerable simplification with respect to the only direct proof presented in the literature.
	theory.stanford.edu /~rvg/abstracts.html (11237 words)

	Scott Smolka's Recent Publications (Site not responding. Last check: 2007-10-08)
		These models are investigated within the context of PCCS, an extension of Milner's SCCS in which each summand of a process summation expression is guarded by a probability and the sum of these probabilities is 1.
		For each model we present a structural operational semantics of PCCS and a notion of bisimulation equivalence which we prove to be a congruence.
		We also provide a polynomial-time reduction in the other direction thereby establishing a kind of equivalence result regarding the expressive power of the two formalisms.
	www.cs.sunysb.edu /~sas/papers (8202 words)

	ipedia.com: Stone-von Neumann theorem Article (Site not responding. Last check: 2007-10-08)
		This statement is usually referred to as the uniqueness of the Weyl form of the canonical commutation relations.
		Then in the previous theorem the direct sum reduces to a single summand.
		Historically this theorem was significant because it was a key step in proving that Heisenberg's matrix mechanics which presents quantum mechanical observables and dynamics in terms of infinite matrices, is unitarily equivalent to Schrödinger's wave mechanical formulation (see Schrödinger picture).
	www.ipedia.com /stone_von_neumann_theorem.html (1022 words)

	Concurrency Abstracts (Site not responding. Last check: 2007-10-08)
		We identify two variants of this approach, a coinductive definition based on final coalgebraic structure in the category of sets, and a direct definition as a final coalgebra in the category of posets.
		The algebra is that of a parallel programming language expanded to the language of full linear logic, Girard's axiomatization of which is satisfied by the event space interpretation of this language.
		Event spaces resemble finite-dimensional vector spaces in distinguishing tensor product from direct product and in being isomorphic to their double dual, but differ from them in distinguishing direct product from direct sum and tensor product from tensor sum.
	boole.stanford.edu /abstracts.html (9620 words)

	GAP Manual: 71 The Specht Share Package
		--Schur algebras (and the general linear groups), although there is less direct support for these algebras.
		Note that the multiplicity of each summand of
		we know the possible indecomposable direct summands of
	schmidt.ucg.ie /gap/CHAP071.htm (7123 words)

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