Direct sums of Rickart modules
Copyright policy )Direct sums of Rickart modules
A right \(R\)-module \(M\) with endomorphism ring \(S=\text{End}_R(M)\) is called a Rickart module if the right annihilator in \(M\) of any single element of \(S\) is a direct summand of \(M\). In general, the class of Rickart modules is not closed under direct sums, and it is interesting to study when it has this closure property. The authors establish several nice results, among which we mention: (1) if a module \(M_i\) is \(M_j\)-injective for all \(i
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Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), Rickart modules, direct summands, Direct sums of modules, Annihilators, Free and projective modules, direct sums of modules, Chain conditions on annihilators and summands: Goldie-type conditions, Rickart (p.p.) rings and modules, Baer rings and modules, right semihereditary rings, Idempotents, Algebra and Number Theory, Right (semi)hereditary, projective modules, free modules, annihilators, Other classes of modules and ideals in associative algebras, Rickart rings, Baer rings, Endomorphisms, endomorphisms, Baer modules, idempotents
Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), Rickart modules, direct summands, Direct sums of modules, Annihilators, Free and projective modules, direct sums of modules, Chain conditions on annihilators and summands: Goldie-type conditions, Rickart (p.p.) rings and modules, Baer rings and modules, right semihereditary rings, Idempotents, Algebra and Number Theory, Right (semi)hereditary, projective modules, free modules, annihilators, Other classes of modules and ideals in associative algebras, Rickart rings, Baer rings, Endomorphisms, endomorphisms, Baer modules, idempotents
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