Indecomposable and Isomorphic Objects in the Category of Monomial Matrices Over a Local Ring

被引:3
作者
Bondarenko, V. M. [1 ]
Bortosh, M. Yu. [1 ]
机构
[1] Ukrainian Natl Acad Sci, Inst Math, Kiev, Ukraine
关键词
SIMILARITY CLASSES; PRINJECTIVE TYPE; POSETS; REPRESENTATIONS; WILD; ALGEBRAS; FORMS; FIELD; TAME;
D O I
10.1007/s11253-017-1413-8
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study the indecomposability and isomorphism of objects from the category of monomial matrices Mmat(K) over a commutative local principal ideal ring K (whose objects are square monomial matrices and the morphisms from X to Y are matrices C such that XC = CY). We also study the subcategory Mmat(0)(K) of the category Mmat(K) with the same objects and solely with morphisms that are monomial matrices.
引用
收藏
页码:1034 / 1050
页数:17
相关论文
共 58 条
[1]  
Arnold D., 1997, C MATH, V74, P299
[2]   Representations of finite posets over discrete valuation rings [J].
Arnold, David M. ;
Simson, Daniel .
COMMUNICATIONS IN ALGEBRA, 2007, 35 (10) :3128-3144
[3]   SIMILARITY CLASSES OF 3 x 3 MATRICES OVER A LOCAL PRINCIPAL IDEAL RING [J].
Avni, Nir ;
Onn, Uri ;
Prasad, Amritanshu ;
Vaserstein, Leonid .
COMMUNICATIONS IN ALGEBRA, 2009, 37 (08) :2601-2615
[4]  
BASHEV VA, 1961, DOKL AKAD NAUK SSSR+, V141, P1015
[5]  
BEKKERT VI, 1986, IZV VUZ MAT+, P62
[6]   The problems of classifying pairs of forms and local algebras with zero cube radical are wild [J].
Belitskii, G ;
Bondarenko, VM ;
Lipyanski, R ;
Plachotnik, VV ;
Sergeichuk, VV .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 402 :135-142
[7]  
Belitskii G, 2009, ELECTRON J LINEAR AL, V18, P516
[8]  
Bondarenko, 1975, MAT SBORNIK, V96, P63
[9]  
Bondarenko V. M., 1977, ZAP NAUCHN SEM LENIG, V71, P24
[10]  
Bondarenko V. M, 1991, ALGEBR ANAL, V3, P38