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For an endomorphism α of a ring R, the endomorphism α is called semicommutative if ab = 0 implies aRα (b) = 0 for a ∈ R. A ring R is called α-semicommutative if there exists a semicommutative endomor-phism α of R. In this paper, various results of semicommutative ringsare extended to α-semicommutative rings. In addition, we introduce thenotion of an α-skew power series Armendariz ring which is an extensionof Armendariz property in a ring R by considering the polynomials in theskew power series ring R[[x;α]]. We show that a number of interestingproperties of a ringR transfer to its the skew power series ringR[[x;α]]and vice-versa such as the Baer property and the p.p.-property, when R is α-skew power series Armendariz. Several known results relating to α-rigid rings can be obtained as corollaries of our results.
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참고문헌 (15)
참고문헌 신청
C. Y. Hong / 2000 / Ore extensions of Baer and p.p.-rings / Journal of Pure and Applied Algebra 151 (3) : 215 ~ 226
C. Y. Hong / 2003 / On skew Armendariz rings / Communications in Algebra 31 (1) : 103 ~ 122
C. Y. Hong / 2005 / Extensions of generalized reduced rings / Algebra Colloquium 12 (2) : 229 ~ 240
C. Y. Hong / 2005 / Rigid ideals and radicals of Ore extensions / Algebra Colloquium 12 (3) : 399 ~ 412
D. D. Anderson / 1999 / Semigroups and rings whose zero products commute / Communications in Algebra 27 (6) : 2847 ~ 2852
C. Y. Hong / 2003 / On skew Armendariz rings / Communications in Algebra 31 (1) : 103 ~ 122
C. Y. Hong / 2005 / Extensions of generalized reduced rings / Algebra Colloquium 12 (2) : 229 ~ 240
C. Y. Hong / 2005 / Rigid ideals and radicals of Ore extensions / Algebra Colloquium 12 (3) : 399 ~ 412
D. D. Anderson / 1999 / Semigroups and rings whose zero products commute / Communications in Algebra 27 (6) : 2847 ~ 2852
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