Addendum to the paper “Corepresentations of Munn matrix algebras”

Authors

DOI:

https://doi.org/10.17721/1812-5409.2023/1.3

Keywords:

corepresentation, generators and defining relations, free associative algebra, non-commutative polynomial, Mann algebra, Rees semigroup, regular sandwich matrix

Abstract

This paper is an addendum to the paper, published in Bulletin of Taras Shevchenko National University of Kyiv (Series: Physics & Mathematics), 2022, No. 3, pp. 42-44.

In the original version does not given a clear definition of the corepresentation of an algebra with identity what led to some formal inaccuracies (regarding notations, writing of defining relations, etc.). All the results of the original paper are essentially correct, but an error was made in the last part of the proof of Theorem 1, which does not affect the correctness of the idea of proof, but requires extended considerations.

In this addendum the author provides detailed information on everything related to statements about the generating elements and defining relations of the Munn algebras over algebras with identity.

Pages of the article in the issue: 26 - 29

Language of the article: English

References

BONDARENKO V. M. (2022) Corepresentations of Munn matrix algebras. Bulletin of University of Kiev (Series: Physics & Mathematics). No. 3. pp. 42-44.

CLIFFORD A. H., PRESTON G. B. (1961) The algebraic theory of semigroups. Vol. 1, American Mathematical Society, Providence, RI, XV+254 pp.

COHN P. M. (1985) Free Algebras and its Relstions, Academic Press Inc, XXii+588 pp.

DRENSKY V. (1999) Free Algebras and PI-Algebras, Springer-Verlag, X+271 pp.

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Published

2023-07-13

How to Cite

Bondarenko, V. M. (2023). Addendum to the paper “Corepresentations of Munn matrix algebras”. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (1), 26–29. https://doi.org/10.17721/1812-5409.2023/1.3

Issue

Section

Algebra, Geometry and Probability Theory