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.

Strongly Rickart Modules

Abstract: In this paper we introduce and study the concept of strongly Rickart modules and strongly CS-Rickart modules as a stronger than of Rickart modules [8] and CS-Rickart modules[3] respectively. A module M is said to be strongly Rickart module if the right annihilators of each single element in S = End R (M) is generated by a left semicentral idempotent in S. A module M is said to be strongly CS- Rickart if for any φ 12∈"> S, r M (φ) is an essential in fully invariant direct summand of M. Properties, results, characterizations and relation of these concepts with others known concepts of modules are studied.

Weak Multiplier Hopf Algebras II: Source and Target Algebras

Abstract: Let (A,Δ) be a weak multiplier Hopf algebra. It is a pair of a non-degenerate algebra A, with or without identity, and a coproduct Δ:A⟶M(A⊗A), satisfying certain properties. In this paper, we continue the study of these objects and construct new examples. A symmetric pair of the source and target maps es and et are studied, and their symmetric pair of images, the source algebra and the target algebra es(A) and et(A), are also investigated. We show that the canonical idempotent E (which is eventually Δ(1)) belongs to the multiplier algebra M(B⊗C), where (B=es(A), C=et(A)) is the symmetric pair of source algebra and target algebra, and also that E is a separability idempotent (as studied). If the weak multiplier Hopf algebra is regular, then also E is a regular separability idempotent. We also see how, for any weak multiplier Hopf algebra (A,Δ), it is possible to make C⊗B (with B and C as above) into a new weak multiplier Hopf algebra. In a sense, it forgets the ’Hopf algebra part’ of the original weak multiplier Hopf algebra and only remembers symmetric pair of the source and target algebras. It is in turn generalized to the case of any symmetric pair of non-degenerate algebras B and C with a separability idempotent E∈M(B⊗C). We get another example using this theory associated to any discrete quantum group. Finally, we also consider the well-known ’quantization’ of the groupoid that comes from an action of a group on a set. All these constructions provide interesting new examples of weak multiplier Hopf algebras (that are not weak Hopf algebras introduced).

Primitive idempotents in central simple algebras over $\mathbb{F}_q(t)$ with an application to coding theory

Abstract: We consider the algorithmic problem of computing a primitive idempotent of a central simple algebra over the field of rational functions over a finite field The algebra is given by a set of structure constants The problem is reduced to the computation of a division algebra Brauer equivalent to the central simple algebra This division algebra is constructed as a cyclic algebra, once the Hasse invariants have been computed We give an application to skew constacyclic convolutional codes

Two-generated idempotent groupoids with small clones

Abstract: A characterization of all classes of idempotent groupoids having no more than two essentially binary term operations with respect to small finite models is given.