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P. M. Cohn called a ring R reversible if whenever ab = 0, then ba = 0 for a, b ε R. 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 α an endomorphism of R, we say that R is right (resp.,left) α-shifting if whenever aα(b) = 0 (resp., α(a)b = 0) for a, b ε R,bα(a) = 0 (resp., α(b)a = 0); and the ring R is called α-shifting if it is both left and right α-shifting. We investigate characterizations of α-shifting rings and their related properties, including the trivial extension,Jordan extension and Dorroh extension. In particular, it is shown that for an automorphism α of a ring R, R is right (resp., left) α-shifting if and only if Q(R) is right (resp., left) ¯α-shifting, whenever there exists the classical right quotient ring Q(R) of R.
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참고문헌 (21)
참고문헌 신청
A. R. Nasr-Isfahani / 2008 / Ore extensions of skew Armendariz rings / Comm. Algebra 36 (2) : 508 ~ 522
C. Y. Hong / 2000 / Ore extensions of Baer and p.p.-rings / J. Pure Appl. Algebra 151 (3) : 215 ~ 226
C. Y. Hong / 2003 / On skew Armendariz rings / Comm. Algebra 31 (1) : 103 ~ 122
C. Y. Hong / 2006 / Extensions of generalized Armendariz rings / Algebra Colloq. 13 (2) : 253 ~ 266
D. A. Jordan / 1982 / Bijective extensions of injective ring endomorphisms / J. London Math. Soc. 25 (3) : 435 ~ 448
C. Y. Hong / 2000 / Ore extensions of Baer and p.p.-rings / J. Pure Appl. Algebra 151 (3) : 215 ~ 226
C. Y. Hong / 2003 / On skew Armendariz rings / Comm. Algebra 31 (1) : 103 ~ 122
C. Y. Hong / 2006 / Extensions of generalized Armendariz rings / Algebra Colloq. 13 (2) : 253 ~ 266
D. A. Jordan / 1982 / Bijective extensions of injective ring endomorphisms / J. London Math. Soc. 25 (3) : 435 ~ 448
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