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For an endomorphism α of a ring R, we introduce the weak α-skew Armendariz rings which are a generalization of the α-skew Armendariz rings and the weak Armendariz rings, and investigate their properties.
Moreover, we prove that a ring R is weak α-skew Armendariz if and only if for any n, the n × n upper triangular matrix ring Tn(R) is weak ¯α-skew Armendariz, where ¯α : Tn(R)→ Tn(R) is an extension of α. If R is reversible and α satisfies the condition that ab = 0 implies aα(b)=0 for any a, b ∈ R, then the ring R[x]/(xn) is weak ¯α-skew Armendariz,where (xn) is an ideal generated by xn, n is a positive integer and ¯α : R[x]/(xn)→ R[x]/(xn) is an extension of α. If α also satisfies the condition that αt = 1 for some positive integer t, the ring R[x] (resp,R[x; α]) is weak ¯α-skew (resp, weak) Armendariz, where ¯α : R[x] → R[x]is an extension of α.
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참고문헌 (9)
참고문헌 신청
C. Huh / 2002 / Armendariz rings and semicommutative rings / Comm. Algebra 30 (2) : 751 ~ 761
C. Y. Hong / 2003 / On skew Armendariz rings / Comm. Algebra 31 (1) : 103 ~ 122
D. D. Anderson / 1998 / Armendariz rings and Gaussian rings / Comm. Algebra 26 (7) : 2265 ~ 2272
E. P. Armendariz / 1974 / A note on extensions of Baer and P.P.-rings / J. Austral. Math. Soc. 18 : 470 ~ 473
J. L. Chen / 2006 / Extensions of injectivity and coherent rings / Comm. Algebra 34 (1) : 275 ~ 288
C. Y. Hong / 2003 / On skew Armendariz rings / Comm. Algebra 31 (1) : 103 ~ 122
D. D. Anderson / 1998 / Armendariz rings and Gaussian rings / Comm. Algebra 26 (7) : 2265 ~ 2272
E. P. Armendariz / 1974 / A note on extensions of Baer and P.P.-rings / J. Austral. Math. Soc. 18 : 470 ~ 473
J. L. Chen / 2006 / Extensions of injectivity and coherent rings / Comm. Algebra 34 (1) : 275 ~ 288
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