Электронный архив

Просмотр по автору "Abyzov A.N."

Просмотр по автору "Abyzov A.N."

Отсортировать по:Сортировать:Результаты поиска на странице:

  • Direct Projective Modules, Direct Injective Modules, and their Generalizations 
    Abyzov A.N.; Tuganbaev A.A.; Tapkin D.T.; Cong Q.T. (2021)
    This paper contains new and previously known results on modules that are close to direct projective and direct injective modules. The main results are presented with proofs.
  • Modules that are Invariant with Respect to Automorphisms and Idempotent Endomorphisms of Their Hulls and Covers 
    Abyzov A.N.; Quynh T.C.; Tuganbaev A.A. (2021)
    The paper contains both known and new results on automorphism-invariant modules, automorphism-coinvariant modules and modules which are invariant or coinvariant with respect to idempotent endomorphisms of its hull and its ...
  • On rings with cyclic almost-injective modules 
    Abyzov A.N.; Quynh T.C. (2021)
    It is shown that every finitely generated right R-module is almost injective if and only if every cyclic right R-module is almost injective, if and only if R/J(R) is a right SV-ring with Loewy(RR) ≤ 2 and there is a finite ...
  • On rings with x<sup>n</sup>- X nilpotent 
    Abyzov A.N.; Tapkin D.T. (2021)
    For n ≥ 2 and for a ring R, the notation Pn(R) means that rn - r is nilpotent for all r ∈ R. In this paper, rings R for which Pn(R) holds are completely characterized for any integers n ≥ 2. This answers a question which ...
  • Retractable and coretractable modules in Wisbauer category 
    Abyzov A.N.; Eryashkin M.S. (2021)
    A right R-module M is called: (1) retractable if HomR(M,N)≠0 for any non-zero submodule N of M; (2) coretractable if HomR(M/N,M)≠0 for any proper submodule N of M. It shows that if M is locally noetherian and every nonzero ...
  • Rings all of whose finitely generated ideals are automorphism-invariant 
    Quynh T.C.; Abyzov A.N.; Trang D.T. (2021)
    Rings in which each finitely generated right ideal is automorphism-invariant (rightfa-rings) are shown to be isomorphic to a formal matrix ring. Among other results it is also shown that (i) if R is a right nonsingular ...
  • Rings over Which Matrices Are Sums of Idempotent and q-Potent Matrices 
    Abyzov A.N.; Tapkin D.T. (2021)
    We study the rings over which each square matrix is the sum of an idempotent matrix and a q-potent matrix. We also show that if F is a finite field not isomorphic to F3 and q > 1 is odd then each square matrix over F is ...
  • Rings Whose Every Right Ideal is a Finite Direct Sum of Automorphism-Invariant Right Ideals 
    Abyzov A.N.; Phan T.H.; Truong C.Q. (2020)
    © 2020, Pleiades Publishing, Ltd. We study the rings R whose every right ideal is a finite direct sum of automorphism-invariant right R-modules. These rings are called right Σ-a-rings. We find a representation in the form ...
  • Rings with x<sup>n</sup>+ x or x<sup>n</sup>- X nilpotent 
    Abyzov A.N.; Danchev P.V.; Tapkin D.T. (2021)
    Let R be a ring and let n be an arbitrary but fixed positive integer. We characterize those rings R whose elements a satisfy at least one of the relations that an + a or an - a is a nilpotent whenever n ϵN\{1}. This extends ...
  • Simple-Direct Modules Over Formal Matrix Rings 
    Abyzov A.N.; Tapkin D.T. (2021)
    Abstract: In the present paper, we study simple-direct-injective modules and simple-direct-projective modules over a formal matrix ring (Formula presented.), where M is an (R,S)-bimodule and N is a (S,R)-bimodule over rings ...
  • When is every matrix over a ring the sum of two tripotents? 
    Abyzov A.N.; Tapkin D.T. (2021)
    We study rings over which every matrix is the sum of two tripotents. In particular, we show that every square matrix over a field F is the sum of two tripotents if and only if F is a prime field with Char(F)≤5.

Поиск в электронном архиве

Просмотр

Моя учетная запись