A ring R is called cleanif every element of R is the sum of a unit and an idempotent. Motivated by a question proposed by Lam on the cleanness of von Neumann Algebras, Vas introduced a more natural concept of cleannes...
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A ring R is called cleanif every element of R is the sum of a unit and an idempotent. Motivated by a question proposed by Lam on the cleanness of von Neumann Algebras, Vas introduced a more natural concept of cleanness for *-rings, called the *-cleanness. More precisely, a *-ring R is called a *-clean ringif every element of R is the sum of a unit and a projection (*-invariant idempotent). Let F be a finite field and G a finite abeliangroup. In this paper, we introduce two classes of involutions on group rings of the form FG and characterize the *-cleanness of these group rings in each case. When * is taken as the classical involution, we also characterize the *-cleanness of F(q)G in terms of LCD abeliancodes and self-orthogonal abeliancodes in F(q)G. (C) 2021 Elsevier Inc. All rights reserved.
Let F be a finite field and let G be a finite group. We show that if C is a G-code over F with dim(F)(C) 2 (see the examples in [1]), we conclude that the smallest dimension of a non-abelian group code over a finite ...
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Let F be a finite field and let G be a finite group. We show that if C is a G-code over F with dim(F)(C) <= 3 then C is an abelian group code. Since there exist non-abelian group codes of dimension 4 when char F > 2 (see the examples in [1]), we conclude that the smallest dimension of a non-abelian group code over a finite field is 4. Published by Elsevier Inc.
We give counterexamples to show that some results regarding equivalence of abelian group codes, that have been in the literature for quite some time, are not correct. Also, we give examples of special families of abel...
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ISBN:
(纸本)9781457704376
We give counterexamples to show that some results regarding equivalence of abelian group codes, that have been in the literature for quite some time, are not correct. Also, we give examples of special families of abeliangroups for which these results do hold.
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