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Co-Coatomically Supplemented Modules
(Ukrainian Mathematical Journal, 2017)
It is shown that if a submodule N of M is co-coatomically supplemented and M/N has no maximal submodule, then M is a co-coatomically supplemented module. If a module M is co-coatomically supplemented, then every finitely ...
Modules and abelian groups with minimal (pure-) projectivity domains
(Journal of Algebra and its Applications, 2017)
In this paper, we give a complete description of the projectively poor abelian groups and prove that there exists a pure projectively poor abelian group. We show that over a commutative Artinian ring every module having a ...
Abelian groups whose nonzero endomorphisms have nonessential kernels
(Journal of Algebra and its Applications, 2017)
In this paper, we describe completely the -singular subgroup of an abelian group and a -nonsingular abelian group in terms of the basic subgroups of its p-components and the quotient group by the torsion part. We also prove ...
Poor and pi-poor Abelian groups
(Communications in Algebra, 2017)
In this paper, poor abelian groups are characterized. It is proved that an abelian group is poor if and only if its torsion part contains a direct summand isomorphic to (Formula presented.) , where P is the set of prime ...
Test modules for flatness
(Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova, 2017)
A right R-module M is said to be a test module for flatness (shortly: an f-test module) provided for each left R-module N, Tor(M, N) = 0 implies N is flat. f-test modules are a flat version of the Whitehead test modules ...
Test modules for flatness
(C E D A M SPA CASA EDITR DOTT ANTONIO MILANI, 2017)
A right R-module M is said to be a test module for flatness (shortly: an f-test module) provided for each left R-module N, Tor(M,N) = 0 implies N is flat. f-test modules are a flat version of the Whitehead test modules for ...
Poor and pi-poor Abelian groups
(TAYLOR & FRANCIS INC, 2017)
In this paper, poor abelian groups are characterized. It is proved that an abelian group is poor if and only if its torsion part contains a direct summand isomorphic to http://www.w3.org/1999/xlink, where P is the set of ...
Modules and abelian groups with minimal (pure-) projectivity domains
(WORLD SCIENTIFIC PUBL CO PTE LTD, 2017)
In this paper, we give a complete description of the projectively poor abelian groups and prove that there exists a pure projectively poor abelian group. We show that over a commutative Artinian ring every module having a ...
Co-Coatomically Supplemented Modules
(SPRINGER, 2017)
It is shown that if a submodule N of M is co-coatomically supplemented and M/N has no maximal submodule, then M is a co-coatomically supplemented module. If a module M is co-coatomically supplemented, then every finitely ...
Abelian groups whose nonzero endomorphisms have nonessential kernels
(WORLD SCIENTIFIC PUBL CO PTE LTD, 2017)
In this paper, we describe completely the K-singular subgroup of an abelian group and a K-nonsingular abelian group in terms of the basic subgroups of its p-components and the quotient group by the torsion part. We also ...