Matrices play an important role in both pure and applied mathematics. Matrices with entries
in rings have been intensively studied and used (eg, see [22, 87]); as well as matrices with …

One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition,
where a module M is called a C3-module if whenever A and B are direct summands of M …

A module M is called a D 4-module if, whenever A and B are submodules of M with M= A⊕
B and f: A→ B is a homomorphism with Im f⊆⊕ B, we have ker f⊆⊕ A. The class of D 4 …

Большое значение матриц для математики и её приложений общеизвестно. Прежде
всего это относится к числовым матрицам. Активно изучаются и используются также …

In this paper, we introduce and study the dual notion of simple-direct-injective modules.
Namely, a right R-module M is called simple-direct-projective if, whenever A and B are …

A right R-module M is called a D 3-module, if M 1 and M 2 are direct summands of M with M=
M 1+ M 2, then M 1∩ M 2 is a direct summand of M. Following the work of Bass on projective …

ABSTRACT A right R-module M is called a U-module if, whenever A and B are submodules
of M with A≅ B and A∩ B= 0, there exist two summands K and L of M such that A⊆ ess K …

In a recent paper, Aydoǧdu and López-Permouth have defined a module M to be N-
subinjective if every homomorphism N→ M extends to some E (N)→ M, where E (N) is the …

[2] Êî÷ åòîâà ÞÂ Декартова сумма решеточно K-упорÿдоченных алгебр//× ебышевский
сборник. 2012. Т. 13, Вып. 1. С. 92-101.[3] Êî÷ åòîâà ÞÂ, Øèðøîâà ÅÅ Первичный радикал …

ABSTRACT A module M is said to be square free if whenever its submodule is isomorphic to
N 2= N⊕ N for some module N, then N= 0. Dually, a module M is said to be d-square free …