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Yahya Talebi

Yahya Talebi

Academic rank: Professor
ORCID: https://orcid.org/0000-0003-2311-4628
Education: PhD.
ScopusId:
HIndex:
Faculty: Faculty of Mathematical Sciences
Address: Dep. Math. University of Mazandaran
Phone: 01135302467

Research

Title
MODULES WITH C∗-CONDITION
Type
JournalPaper
Keywords
Lifting module, Co-singular module, Projective module, Injective module
Year
2009
Journal TAIWANESE JOURNAL OF MATHEMATICS
DOI
Researchers Yahya Talebi ، M. Javad Nematollahi

Abstract

Through this paper R is an associative ring with identity and all modules are unitary right R-modules. A submodule N of a module M is called small in M (denoted by Nl−/M) if for every proper submodule L of M, N + L = M. M is called a small module if M is small in some modules [1]. In [1] Leonard has proved that a module M is a small module if and only if it is small in its injective hull. For a module M let Z(M) = Rej(M, S) = {Kerf | f : M → S, S ∈ S} = {U ⊆ M | M/U ∈ S} where S denotes the class of all small modules. M is called cosingular if Z(M) = 0. It is obvious that every small module is cosingular but in general the converse is not true. A module M has C∗ if every submodule N of M contains a direct summand K of M such that N/K is cosingular. Finally we recall that a module M is lifting if every submodule N of M contains a direct summand K of M such that N/Kl−/M/K.