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On weak Rickart modules

Tutuncu, Derya Keskin; Ertas, Nil Orhan; Tribak, Rachid


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    <subfield code="a">We introduce and study the notion of w-Rickart modules (i.e. modules M such that for every nonzero endomorphism phi of M, the kernel of phi is contained in a proper direct summand of M). We show that the class of right w-Rickart modules lies properly between the class of right K-nonsingular modules and the class of right Rickart modules. Many properties of w-Rickart modules are established. Some relevant counterexamples are indicated.</subfield>
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