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RING ENDOMORPHISMS WITH THE REVERSIBLE CONDITION
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 Title & Authors
RING ENDOMORPHISMS WITH THE REVERSIBLE CONDITION
Baser, Muhittin; Kaynarca, Fatma; Kwak, Tai-Keun;
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 Abstract
P. M. Cohn called a ring R reversible if whenever ab = 0, then ba = 0 for a, . Commutative rings and reduced rings are reversible. In this paper, we extend the reversible condition of a ring as follows: Let R be a ring and an endomorphism of R, we say that R is right (resp., left) -shifting if whenever (resp., ) for a, , (resp., ); and the ring R is called -shifting if it is both left and right -shifting. We investigate characterizations of -shifting rings and their related properties, including the trivial extension, Jordan extension and Dorroh extension. In particular, it is shown that for an automorphism of a ring R, R is right (resp., left) -shifting if and only if Q(R) is right (resp., left) -shifting, whenever there exists the classical right quotient ring Q(R) of R.
 Keywords
ring endomorphism;reduced ring;reversible ring;trivial extension;classical right quotient ring;
 Language
English
 Cited by
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