matrix rings
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2022 ◽  
Vol 345 (1) ◽  
pp. 112671
Author(s):  
Bocong Chen ◽  
Jing Huang
Keyword(s):  

2021 ◽  
Vol 76 ◽  
pp. 101924
Author(s):  
Adrian Korban ◽  
Serap Şahinkaya ◽  
Deniz Ustun
Keyword(s):  

CAUCHY ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 129-135
Author(s):  
Ahmad Faisol ◽  
Fitriani Fitriani

Let  M_n (R_1 [[S_1,≤_1,ω_1]]) and M_n (R_2 [[S_2,≤_2,ω_2]]) be a matrix rings over skew generalized power series rings, where R_1,R_2 are commutative rings with an identity element, (S_1,≤_1 ),(S_2,≤_2 ) are strictly ordered monoids, ω_1:S_1→End(R_1 ),〖 ω〗_2:S_2→End(R_2 ) are monoid homomorphisms. In this research, a mapping  τ from M_n (R_1 [[S_1,≤_1,ω_1]]) to M_n (R_2 [[S_2,≤_2,ω_2]]) is defined by using a strictly ordered monoid homomorphism δ:(S_1,≤_1 )→(S_2,≤_2 ), and ring homomorphisms μ:R_1→R_2 and σ:R_1 [[S_1,≤_1,ω_1]]→R_2 [[S_2,≤_2,ω_2]]. Furthermore, it is proved that τ is a ring homomorphism, and also the sufficient conditions for  τ to be a monomorphism, epimorphism, and isomorphism are given.


2021 ◽  
Vol 28 (04) ◽  
pp. 625-634
Author(s):  
Aleksandra S. Kostić ◽  
Zoran Z. Petrović ◽  
Zoran S. Pucanović ◽  
Maja Roslavcev

Let [Formula: see text] be an associative unital ring and not necessarily commutative. We analyze conditions under which every [Formula: see text] matrix [Formula: see text] over [Formula: see text] is expressible as a sum [Formula: see text] of (commuting) idempotent matrices [Formula: see text] and a nilpotent matrix [Formula: see text].


Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2676
Author(s):  
Driss Bennis ◽  
Rachid El Maaouy ◽  
Juan Ramón García Rozas ◽  
Luis Oyonarte

Let A and B be rings, U a (B,A)-bimodule, and T=A0UB the triangular matrix ring. In this paper, several notions in relative Gorenstein algebra over a triangular matrix ring are investigated. We first study how to construct w-tilting (tilting, semidualizing) over T using the corresponding ones over A and B. We show that when U is relative (weakly) compatible, we are able to describe the structure of GC-projective modules over T. As an application, we study when a morphism in T-Mod is a special GCP(T)-precover and when the class GCP(T) is a special precovering class. In addition, we study the relative global dimension of T. In some cases, we show that it can be computed from the relative global dimensions of A and B. We end the paper with a counterexample to a result that characterizes when a T-module has a finite projective dimension.


2021 ◽  
Vol 258 (2) ◽  
pp. 222-249
Author(s):  
P. A. Krylov ◽  
A. A. Tuganbaev

Author(s):  
Figen Takil Mutlu ◽  
Adnan Tercan

In this paper, we define a module [Formula: see text] to be [Formula: see text] if and only if intersection of each pair of [Formula: see text]-closed direct summands is also a direct summand of [Formula: see text]. We investigate structural properties of [Formula: see text]-modules and locate the implications between the other module properties which are essentially based on direct summands. We deal with decomposition theory as well as direct summands of [Formula: see text]-modules. We apply our results to matrix rings. To this end, it is obtained that the [Formula: see text] property is not Morita invariant.


2021 ◽  
Vol 225 (8) ◽  
pp. 106633
Author(s):  
Tyler B. Bowles ◽  
Dariusz M. Wilczyński

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