Trace 1, 2×2 matrices over principal ideal domains are exchange

Author:

CALUGAREANU GRIGORE1,F. POP HORIA2

Affiliation:

1. DEPARTMENT OF MATHEMATICS BABES¸ -BOLYAI UNIVERSITY

2. DEPARTMENT OF COMPUTER SCIENCE BABES¸ -BOLYAI UNIVERSITY

Abstract

We prove that trace 1 matrices over principal ideal domains are exchange and characterize 2 × 2 exchange matrices over commutative domains. In addition, we emphasize large classes of not exchange 2 × 2 and 3 × 3 integral matrices.

Publisher

Technical University of Cluj Napoca, North University Center of Baia Mare

Subject

General Mathematics

Reference9 articles.

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2. [2] Andrica, D. and Calug ˘ areanu, G., ˘ Uniquely clean 2 × 2 invertible integral matrices, Studia Universitatis Babes¸-Bolyai, 62 (2017), No. 3, 287–293

3. [3] Calug ˘ areanu, G., ˘ Tripotents: a class of strongly clean elements in rings, An. S¸ t. Univ. Ovidius Constant¸a, 26 (2018), No. 1, 69–80

4. [4] Calug ˘ areanu, G., ˘ Clean integral 2 × 2 matrices, Studia Sci. Math. Hungarica, 55 (2018), No. 1, 41–52

5. [5] Calug ˘ areanu, G., ˘ Nil-clean integral 2 × 2 matrices: The elliptic case, Bull. Math. Soc. Sci. Roum., 62 (110) (2019), No. 3, 239–250

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1. Are nil-clean 3 × 3 integral matrices, exchange?;Annals of the Alexandru Ioan Cuza University - Mathematics;2021

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