1 Ocak 2014 Dergi makalesi Açık Erişim

Keskin Tutuncu, Derya; Orhan Ertas, Nil; Smith, Patrick F.; Tribak, Rachid

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    <subfield code="a">The snbmodule (Z)overbar(M) = boolean AND{N vertical bar M/N is small in its injective hull} was introduced by Talebi and Vanaja in 2002. A ring R is said to have property (P) if (Z)overbar(M) is a direct summand of M for every R-module M. It is shown that a commutative perfect ring R has (P) if and only if R is semisimple. An example is given to show that this characterization is not true for noncommutative rings. We prove that if R is a commutative ring such that the class {M is an element of Mod-R vertical bar &amp;lt;(Z)overbar &amp;gt;(R)(M) = 0} is closed under factor modules, then R has (P) if and only if the ring R is von Neumann regular.</subfield>
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