Topic
Idempotence
About: Idempotence is a research topic. Over the lifetime, 1860 publications have been published within this topic receiving 19976 citations. The topic is also known as: idempotent.
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TL;DR: In this paper, the notion of a sequentially dense monomorphism is used to describe the s-injective hull of acts over an idempotent semigroup.
Abstract: In this paper using the notion of a sequentially dense monomorphism we consider sequential injectivity (s-injectivity) for acts over a semigroup S. Among other things we describe the s-injective hull of acts over an idempotent semigroup S. We also give some classes of idempotent semigroups for the acts over which the notions of injectivity and s-injectivity coincide, and hence get the injective hull of acts over these classes of semigroups.
5 citations
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TL;DR: In this paper, it was shown that every locally idempotent (locally m-pseudoconvex) Hausdor algebra A with pseudoconvex vonNeumann bornology is a regular (respectively, bornological) inductive limit of metrizable locally m-(kB-convex)-subalgebras AB of AB of A.
Abstract: It is shown that every locally idempotent (locally m-pseudoconvex) Hausdor algebra A with pseudoconvex vonNeumannbornologyis a regular (respectively, bornological) inductive limit of metrizable locally m-(kB-convex) subalgebras AB of A In the case where A, in addition, is sequentially BA-complete (sequentially advertibly complete), then every subalgebraAB is a locally m-(kB-convex) Frechet algebra (respectively, an advertibly complete metrizable locally m-(kB-convex) algebra) for some kB 2 (0,1) Moreover, for a commutative unital locally m-pseudoconvex Hausdor algebra A over C with pseudoconvex von Neumann bornology, which at the same time is sequentially BA-complete and advertibly complete, the statements (a)-(j) of Proposition 32 are equivalent
5 citations
01 Jan 2006
TL;DR: In this paper, a chain of proper inclusions of all n-idempotents, all generalized nidempotent, and all hyper-generalized n-empotents is obtained.
Abstract: For an integer n≥2,we say that an operator A is an n-idempotent if A~n=A;A is a generalized n-idempotent if A~n=A~*;A is a hyper-generalized n- iclempotent if A~n=A~+.The set of all n-idempotents,all generalized n-idempotents and all hyper-generalized n-idempotents are denoted by I_n(H),GI_n(H)and HGI_n(H),respectively.In this note,we obtain a chain of proper inclusions GI_n(H)HGI_n(H)I_(n+2)(H).
5 citations
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TL;DR: In this article, it was shown that if a finite dimension algebra over an algebraically closed field has projective ideals, then there are infinitely many nonisomorphic indecomposable modules of infinite projective dimension.
Abstract: Let $A$ be a finite dimension algebra over an algebraically closed field such that all its idempotent ideals are projective. We show that if $A$ is representation-infinite and not hereditary, then there exist infinitely many nonisomorphic indecomposable $A$-modules of infinite projective dimension.
5 citations
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5 citations