Ore Extensions of Skew Armendariz Rings

REFERENCES

• Anderson , D. D. , Camillo , V. ( 1998 ). Armendariz rings and Gaussian rings . Comm. Algebra 26 ( 7 ): 2265 – 2275 .
   Web of Science ®Google Scholar
• Armendariz , E. P. ( 1974 ). A note on extensions of Baer and p.p.-rings . J. Austral. Math. Soc. 18 : 470 – 473 .
   Google Scholar
• Armendariz , E. P. , Koo , H. K. , Park , J. K. ( 1987 ). Isomorphic ore extensions . Comm. Algebra 15 : 2633 – 2652 .
   Web of Science ®Google Scholar
• Bell , H. E. ( 1970 ). Near-rings in which each element is a power of itself . Bull. Australian Math. Soc. 2 : 363 – 368 .
   Google Scholar
• Birkenmeier , G. F. , Kim , J. Y. , Park , J. K. ( 2000 ). On polynomial extensions of principally quasi-Baer rings . Kyungpook Math. J. 40 : 247 – 253 .
   Google Scholar
• Birkenmeier , G. F. , Kim , J. Y. , Park , J. K. ( 2001a ). Principally quasi-Baer rings . Comm. Algebra 29 ( 2 ): 639 – 660 .
   Web of Science ®Google Scholar
• Birkenmeier , G. F. , Kim , J. Y. , Park , J. K. ( 2001b ). Polynomial extensions of Baer and quasi-Baer rings . J. Pure Appl. Algebra 159 : 24 – 42 .
   Web of Science ®Google Scholar
• Clark , W. E. ( 1967 ). Twisted matrix units semigroup algebras . Duke Math. J. 34 : 417 – 424 .
   Web of Science ®Google Scholar
• Goodearl , K. R. , Warfield , R. B. ( 1989 ). An Introduction to Noncommutative Noetherian Rings . Cambridge : Cambridge University Press .
   Google Scholar
• Han , J. , Hirano , Y. , Kim , H. ( 2000 ). Semiprime ore extensions . Comm. in Algebra 28 ( 8 ): 3795 – 3801 .
   Web of Science ®Google Scholar
• Hashemi , E. , Moussavi , A. ( 2005 ). Polynomial extensions of quasi-Baer rings . Acta Math. Hungar. 107 ( 3 ): 207 – 224 .
   Web of Science ®Google Scholar
• Hashemi , E. , Moussavi , A. , Haj Seyyed Javadi , H. ( 2003 ). Polynomial ore extensions of Baer and p.p.-rings . Bull. Iranian Math. Soc. 29 ( 2 ): 65 – 86 .
   Google Scholar
• Hirano , Y. ( 2001 ). On ordered monoid rings over a quasi-Baer ring . Comm. Algebra 29 ( 5 ): 2089 – 2095 .
   Web of Science ®Google Scholar
• Hirano , Y. ( 2002 ). On annihilator ideals of a polynomial ring over a noncommutative ring . J. Pure Appl. Algebra 168 : 45 – 52 .
   Web of Science ®Google Scholar
• Hong , C. Y. , Kim , N. K. , Kwak , T. K. ( 2000 ). Ore extensions of Baer and p.p.-rings . J. Pure Appl. Algebra 151 : 215 – 226 .
   Web of Science ®Google Scholar
• Hong , C. Y. , Kim , N. K. , Kwak , T. K. ( 2003 ). On skew Armendariz rings . Comm. Algebra 31 ( 1 ): 103 – 122 .
   Web of Science ®Google Scholar
• Huh , C. , Lee , Y. , Smoktunowicz , A. ( 2002 ). Armendariz rings and semicommutative rings . Comm. Algebra 30 ( 2 ): 751 – 761 .
   Web of Science ®Google Scholar
• Kaplansky , I. ( 1965 ). Rings of Operators . New York : Benjamin .
   Google Scholar
• Kerr , J. W. ( 1990 ). The polynomial ring over a Goldie ring need not be a Goldie ring . J. Algebra 134 : 344 – 352 .
   Web of Science ®Google Scholar
• Kim , N. K. , Lee , Y. ( 2000 ). Armendariz rings and reduced rings . J. Algebra 223 : 477 – 488 .
   Web of Science ®Google Scholar
• Krempa , J. ( 1996 ). Some examples of reduced rings . Algebra Colloq. 3 ( 4 ): 289 – 300 .
   Google Scholar
• Lee , T. K. , Wong , T. L. ( 2003 ). On Armendariz rings . Houston J. Math. 29 ( 3 ): 583 – 593 .
   Web of Science ®Google Scholar
• Matczuk , J. ( 2004 ). A characterization of σ-rigid rings . Comm. Algebra 32 ( 11 ): 4333 – 4336 .
   Web of Science ®Google Scholar
• Moussavi , A. , Hashemi , E. ( 2005 ). On (α, δ)-skew Armendariz rings . J. Korean Math. Soc. 42 ( 2 ): 353 – 363 .
   Web of Science ®Google Scholar
• Pollingher , P. , Zaks , A. ( 1970 ). On Baer and quasi-Baer rings . Duke Math. J. 37 : 127 – 138 .
   Web of Science ®Google Scholar
• Rege , M. B. , Chhawchharia , S. ( 1997 ). Armendariz rings . Proc. Japan Acad. Ser. A Math. Sci. 73 : 14 – 17 .
   Google Scholar
• Zhong-kui , L. , Wei li , F. ( 2005 ). Principal quasi-Baerness of skew power series rings . J. Math. Res. Exposition 25 ( 2 ): 197 – 203 .
   Google Scholar
• Communicated by V. A. Artamonov.
   Google Scholar