Rings, matrices over which are representable as the sum of two potent matrices
https://doi.org/10.26907/0021-3446-2023-12-90-94
Abstract
This paper investigates conditions under which representability of each element a from the field P as the sum a = f + g, with f q1 = f, g q2 = g and q1, q2 are fixed integers >1, implies a similar representability of each square matrix over the field P. We propose a general approach to solving this problem. As an application we describe fields and commutative rings with 2 is a unit, over which each square matrix is the sum of two 4-potent matrices.
About the Authors
A. N. Abyzov
Kazan Federal University
Russian Federation
Russian Federation
Adel Nailevich Abyzov
18 Kremlyovskaya str., Kazan, 420008
D. T. Tapkin
Kazan Federal University
Russian Federation
Russian Federation
Danil’ Tagirzyanovich Tapkin
18 Kremlyovskaya str., Kazan, 420008
References
1. Hirano Y., Tominaga H. Rings in which every element is the sum of two idempotents, Bull. Aust. Math. Soc. 37 (2), 161–164 (1988).
2. Tang G., Zhou Y., Su H. Matrices over a commutative ring as sums of three idempotents or three involutions, Linear Multilinear Algebra 67 (2), 267–277 (2019).
3. Абызов А.Н., Мухаметгалиев М.И. О некоторых матричных аналогах малой теоремы Ферма, Матем. заметки 101 (2), 163–168 (2017).
4. Абызов А.Н., Тапкин Д.Т. Кольца, матрицы над которыми представимы в виде суммы идемпотентной матриы и q-потентной матрицы, Сиб. матем. журн. 62 (1), 3–18 (2021).
5. Abyzov A.N., Tapkin D.T. When is every matrix over a ring the sum of two tripotents? Linear Algebra and Appl. 630 (3), 316–325 (2021).
Review
For citations:
Abyzov A.N., Tapkin D.T. Rings, matrices over which are representable as the sum of two potent matrices. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2023;1(12):90-94. (In Russ.) https://doi.org/10.26907/0021-3446-2023-12-90-94
Views:
133
Email this article 