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A ring R is called reversibly Armendariz if bjai = 0for all i; j whenever f(x)g(x) Σ = 0 for two polynomials f(x) = m i=0 aixi; g(x) =Σn j=0 bjxj over R. It is proved that a ring R is reversibly Armendariz if and only if its polynomial ring is re-versibly Armendariz if and only if its Laurent polynomial ring is re-versibly Armendariz. Relations between reversibly Armendariz rings and related ring properties are examined in this note, observing the structures of many examples concerned. Various kinds of reversibly Armendariz rings are provided in the process. Especially it is shown to be possible to construct reversibly Armendariz rings from given any Armendariz rings.
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참고문헌 (19)
참고문헌 신청
C. Huh / 2002 / Armendariz rings and semicommutative rings / Comm. Algebra 30 : 751 ~ 761
C. Huh / 2005 / Basic examples and extensions of symmetric rings / JOURNAL OF PURE AND APPLIED ALGEBRA 202 : 154 ~ 167
D.D. Anderson / 1998 / Armendariz rings and Gaussian rings / Comm. Al- gebra 26 : 2265 ~ 2272
D.D. Anderson / 1999 / Semigroups and rings whose zero products commute / Comm. Algebra 27 : 2847 ~ 2852
E.P. Armendariz / 1974 / A note on extensions of Baer and P.P.-rings / J. Aust. Math. Soc 18 : 470 ~ 473
C. Huh / 2005 / Basic examples and extensions of symmetric rings / JOURNAL OF PURE AND APPLIED ALGEBRA 202 : 154 ~ 167
D.D. Anderson / 1998 / Armendariz rings and Gaussian rings / Comm. Al- gebra 26 : 2265 ~ 2272
D.D. Anderson / 1999 / Semigroups and rings whose zero products commute / Comm. Algebra 27 : 2847 ~ 2852
E.P. Armendariz / 1974 / A note on extensions of Baer and P.P.-rings / J. Aust. Math. Soc 18 : 470 ~ 473
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