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Non-Negative Integer Matrix Representations of a Z+-Ring

Non-Negative Integer Matrix Representations of a $\mathbb{Z}_{+}$-Ring

Year:    2021

Author:    Zhichao Chen, Jiayi Cai, Lingchao Meng, Libin Li

Journal of Mathematical Study, Vol. 54 (2021), Iss. 4 : pp. 357–370

Abstract

The Z+-ring is an important invariant in the theory of tensor category. In this paper, by using matrix method, we describe all irreducible Z+-modules over a Z+-ring A, where A is a commutative ring with a Z+-basis{1, x, y, xy} and relations: x2=1,y2=1+x+xy.We prove that when the rank of Z+-module n5, there does not exist irreducible Z+-modules and when the rank n4, there exists finite inequivalent irreducible Z+-modules, the number of which is respectively 1, 3, 3, 2 when the rank runs from 1 to 4.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v54n4.21.02

Journal of Mathematical Study, Vol. 54 (2021), Iss. 4 : pp. 357–370

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Non-negative integer matrix representation irreducible Z+-module Z+-ring.

Author Details

Zhichao Chen Email

Jiayi Cai Email

Lingchao Meng Email

Libin Li Email

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