Number theory of matrix semigroups

被引：16

作者：

Baeth, Nicholas ^{[1
]}

Ponomarenko, Vadim ^{[2
]}

Adams, Donald

Ardila, Rene ^{[3
]}

Hannasch, David ^{[4
]}

Kosh, Audra ^{[5
]}

McCarthy, Hanah ^{[6
]}

Rosenbaum, Ryan

机构：

[1] Univ Cent Missouri, Dept Math & Comp Sci, Warrensburg, MO 64093 USA

[2] San Diego State Univ, Dept Math & Stat, San Diego, CA 92182 USA

[3] CUNY City Coll, New York, NY 10031 USA

[4] Univ Nevada, Las Vegas, NV 89154 USA

[5] Univ Calif Santa Barbara, Santa Barbara, CA 93106 USA

[6] Lawrence Univ, Appleton, WI 54911 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2011年 / 434卷 / 03期

关键词：

Matrix semigroups; Factorization; Integral-valued matrices; FACTORIZATION;

D O I：

10.1016/j.laa.2010.09.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Unlike factorization theory of commutative semigroups which are well-studied, very little literature exists describing factorization properties in noncommutative semigroups. Perhaps the most ubiquitous noncommutative semigroups are semigroups of square matrices and this article investigates the factorization properties within certain subsemigroups of M(n)(Z), the semigroup of n x n matrices with integer entries. Certain important invariants are calculated to give a sense of how unique or non-unique factorization is in each of these semigroups. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：694 / 711

页数：18

共 21 条

[1]

ADAMS D, 2009, BIFURCUS SEMIGROUPS, V2, P351

[2]

Ch'uan J. C., 1985, LINEAR MULTILINEAR A, V18, P213

[3]

Ch'uan J. C., 1986, B I MATH ACAD SINICA, V14, P11

[4]

Cohn P. M., 1963, T AM MATH SOC, V109, P313, DOI DOI 10.1090/S0002-9947-1963-0155851-X

[5] FACTORIZATION IN HEREDITARY ORDERS [J].

ESTES, DR .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1991, 157 :161-164

[6]

FRUMKIN MA, 1987, COMPUTATIONSAL PROCE, V5, P302

[7]

Geroldinger A., 2006, PURE APPL MATH

[8]

Golub G. H., 1996, MATRIX COMPUTATIONS

[9]

GRACINDA HS, 2006, COMMUN ALGEBRA, V34, P1213

[10] NON-UNIQUE FACTORIZATION IN SUBSEMIGROUPS OF SEMIGROUPS WITH UNIQUE PRIME FACTORIZATION [J].

GREITER, G .

AMERICAN MATHEMATICAL MONTHLY, 1980, 87 (06) :473-474

← 1 2 3 →