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Weak Quasi-Armendariz Rings

Muhittin Başer

Department of Mathematics, Kocatepe University, Afyonkarahisar 03200, Turkey

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Fatma Kaynarca

Department of Mathematics, Kocatepe University, Afyonkarahisar 03200, Turkey

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Tai Keun Kwak

Department of Mathematics, Daejin University, Pocheon 487-711, Korea

Corresponding author.

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, and

Yang Lee

Department of Mathematics, Pusan National University, Pusan 609-735, Korea

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https://doi.org/10.1142/S1005386711000423Cited by:5 (Source: Crossref)

Abstract

In this paper, we introduce and study weak quasi-Armendariz rings which unify the notions of weak Armendariz rings and quasi-Armendariz rings. It is shown that the weak quasi-Armendarizness is a Morita invariant property. For a semiprime ring R, it is shown that R[x]/〈xⁿ〉 is weak quasi-Armendariz, where R[x] is the polynomial ring over R and 〈xⁿ〉 is the ideal of R[x] generated by xⁿ. Various properties of weak quasi-Armendariz rings are also observed.

Keywords:

AMSC: 16N60, 16S36

References

D. D. Anderson and V. Camillo, Comm. Algebra 26(7), 2265 (1998), DOI: 10.1080/00927879808826274. Crossref, Web of Science, Google Scholar
E. P. Armendariz, J. Austral. Math. Soc. 18, 470 (1974), DOI: 10.1017/S1446788700029190. Crossref, Web of Science, Google Scholar
G. F. Birkenmeier, J. Y. Kim and J. K. Park, Comm. Algebra 29(2), 639 (2001), DOI: 10.1081/AGB-100001530. Crossref, Web of Science, Google Scholar
W. E. Clark, Duke Math. J. 34, 417 (1967), DOI: 10.1215/S0012-7094-67-03446-1. Crossref, Web of Science, Google Scholar
Y. Hirano, J. Pure Appl. Algebra 168, 45 (2002), DOI: 10.1016/S0022-4049(01)00053-6. Crossref, Web of Science, Google Scholar
C. Y. Hong, N. K. Kim and T. K. Kwak, J. Pure Appl. Algebra 151, 215 (2000), DOI: 10.1016/S0022-4049(99)00020-1. Crossref, Web of Science, Google Scholar
C. Huh, Y. Lee and A. Smoktunowicz, Comm. Algebra 30, 751 (2002), DOI: 10.1081/AGB-120013179. Crossref, Web of Science, Google Scholar
I. Kaplansky , Rings of Operators ( W.A. Benjamin , New York , 1968 ) . Google Scholar
N. K. Kim and Y. Lee, J. Algebra 223, 477 (2000), DOI: 10.1006/jabr.1999.8017. Crossref, Web of Science, Google Scholar
T. Y. Lam , A First Course in Noncommutative Rings ( Springer-Verlag , New York , 1991 ) . Crossref, Google Scholar
T. K. Lee and T. L. Wong, Houston J. Math. 29, 583 (2003). Web of Science, Google Scholar
T. K. Lee and Y. Q. Zhou, Comm. Algebra 32, 2287 (2004), DOI: 10.1081/AGB-120037221. Crossref, Web of Science, Google Scholar
M. B. Rege and S. Chhawchharia, Proc. Japan Acad. (Ser. A Math. Sci.) 73, 14 (1997), DOI: 10.3792/pjaa.73.14. Crossref, Web of Science, Google Scholar
J. C. Shepherdson, Proc. London Math. Soc. 3, 71 (1951). Google Scholar
G. Y. Shin, Trans. Amer. Math. Soc. 184, 43 (1973), DOI: 10.1090/S0002-9947-1973-0338058-9. Crossref, Web of Science, Google Scholar