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P. M. Cohn called a ring R reversible if whenever ab=0,then ba=0 for a, b ∈ R. In this paper, we study an extension of a reversible ring with its endomorphism. An endomorphism α of a ring R is called strong right (resp.,left) reversible if whenever aα(b)=0 (resp.,aα(a)b=0) for a, b ∈ R, ba=0. A ring R is called strong right (resp., left)α-reversible if there exists a strong right (resp., left)reversible endomorphism α of R, and the ring R is called strong α-reversible if R is both strong left and right α-reversible. We investigate characterizations of strong α-reversible rings and their related properties including extensions. In particular, we show that every semiprime and strong α-reversible ring is α-rigid and that for an α-skew Armendariz ring R, the ring R is reversible and strong α-reversible if and only if the skew polynomial ring R[x;α] of R is reversible.
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참고문헌 (10)
참고문헌 신청
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 / 2005 / Extensions of generalized reduced rings / Algebra Colloq. 12 (2) : 229 ~ 240
D. A. Jordan / 1982 / Bijective extensions of injective rings endomorphism / J. Lond. Math. Soc. 25 : 435 ~ 448
J. Krempa / 1996 / Some examples of reduced rings / Algebra Colloq. 3 (4) : 289 ~ 300
C. Y. Hong / 2003 / On Skew Armendariz Rings / Comm. Algebra 31 (1) : 103 ~ 122
C. Y. Hong / 2005 / Extensions of generalized reduced rings / Algebra Colloq. 12 (2) : 229 ~ 240
D. A. Jordan / 1982 / Bijective extensions of injective rings endomorphism / J. Lond. Math. Soc. 25 : 435 ~ 448
J. Krempa / 1996 / Some examples of reduced rings / Algebra Colloq. 3 (4) : 289 ~ 300
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