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On the construction and the realization of wild monoids

Pavel Růžička (2018)

Archivum Mathematicum

We develop elementary methods of computing the monoid 𝒱 ( R ) for a directly-finite regular ring R . We construct a class of directly finite non-cancellative refinement monoids and realize them by regular algebras over an arbitrary field.

On the derived length of units in group algebra

Dishari Chaudhuri, Anupam Saikia (2017)

Czechoslovak Mathematical Journal

Let G be a finite group G , K a field of characteristic p 17 and let U be the group of units in K G . We show that if the derived length of U does not exceed 4 , then G must be abelian.

On the Drazin index of regular elements

Pedro Patrício, António Costa (2009)

Open Mathematics

It is known that the existence of the group inverse a # of a ring element a is equivalent to the invertibility of a 2 a − + 1 − aa −, independently of the choice of the von Neumann inverse a − of a. In this paper, we relate the Drazin index of a to the Drazin index of a 2 a − + 1 − aa −. We give an alternative characterization when considering matrices over an algebraically closed field. We close with some questions and remarks.

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