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Просмотр по автору "Abyzov A."

Просмотр по автору "Abyzov A."

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  • Regular semiartinian rings 
    Abyzov A. (2012)
    We study the structure of rings over which every right module is an essential extension of a semisimple module by an injective one. A ring R is called a right max-ring if every nonzero right R-module has a maximal submodule. ...
  • Retractable and Coretractable Modules 
    Abyzov A.; Tuganbaev A. (2016)
    © 2016, Springer Science+Business Media New York.In this paper, we study mod-retractable modules, CSL-modules, fully Kasch modules, and their interrelations. Right fully Kasch rings are described. It is proved that for a ...
  • Retractable and Coretractable Modules 
    Abyzov A.; Tuganbaev A. (2016)
    © 2016 Springer Science+Business Media New York In this paper, we study mod-retractable modules, CSL-modules, fully Kasch modules, and their interrelations. Right fully Kasch rings are described. It is proved that for a ...
  • Rings Characterized via Some Classes of Almost-Injective Modules 
    Quynh T.C.; Abyzov A.; Dan P.; Van Thuyet L. (2020)
    © 2020, Iranian Mathematical Society. In this paper, we study rings with the property that every cyclic module is almost-injective (CAI). It is shown that R is an Artinian serial ring with J(R) 2= 0 if and only if R is a ...
  • Rings of formal matrices close to regular 
    Abyzov A. (2015)
    © 2015, Allerton Press, Inc. We give a description of rings of formalmatrices belonging to one of the following classes of rings: semiartinian rings, max-rings, V -rings, SV -rings. We study semiartinian SSP-rings and ...
  • Rings over which all modules are I0-modules. II 
    Abyzov A.; Tuganbaev A. (2009)
    All right R-modules are I0-modules if and only if either R is a right SV-ring or R/I(2) (R) is an Artinian serial ring such that the square of the Jacobson radical of R/I(2) (R) is equal to zero. © 2009 Springer Science+Business ...
  • Rings over which every module is an I*<inf>0</inf>-module 
    Abyzov A. (2017)
    © 2017, Allerton Press, Inc. We obtain a description of semi-artinian rings over which every module is an I* 0 -module. We also describe semi-artinian rings over which every module is a direct sum of a projective module ...
  • Semisimple-direct-injective modules 
    Abyzov A.; Koşan T.; Quynh T.C.; Tapkin D. (2021)
    The notion of simple-direct-injective modules which are a generalization of injective modules unifies C2 and C3-modules. In the present paper, we introduce the notion of the semisimple-direct-injective module which gives ...
  • SSP rings and modules 
    Abyzov A.; Quynh T.; Nhan T. (2016)
    © World Scientific Publishing Company.We study A-Ci modules (i = 2, 3), first introduced in [K. Oshiro, Continuous modules and quasi-continuous modules, Osaka J. Math. 20 (1983) 681-694], and A-SSP modules. We consider the ...
  • Strongly q-Nil-Clean Rings 
    Abyzov A. (2019)
    © 2019, Pleiades Publishing, Ltd. Under study are the rings whose every element is a sum of a nilpotent and a q-potent that commute with one another. We describe the rings whose every element is a sum of k idempotents (for ...
  • Weakly regular modules over normal rings 
    Abyzov A. (2008)
    Under study are some conditions for the weakly regular modules to be closed under direct sums and the rings over which all modules are weakly regular. For an arbitrary right R-module M, we prove that every module in the ...

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