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DIFFERENTIAL POLYNOMIALS OVER BAER RINGS

Year 2009, Volume: 6 Issue: 6, 38 - 45, 01.12.2009

Ebrahim Hashemi

Abstract

Let R be a ring with unity and δ a derivation on R. In this paper we extend a result of Armendariz on the Baer condition in a polynomial ring to a Baer condition in a nearring of differential polynomial. The nearring of differential has substitution for its ”multiplication” operation.

Keywords

annihilator conditions nearrings derivation polynomial rings Baer rings Armendariz rings

References

  • E.P. Armendariz, A note on extensions of Baer and p.p.-rings, J. Austral. Math. Soc. 18 (1974), 470-473.
  • S.K. Berberian, Baer *-rings, Springer-Verlag, Berlin, 1968.
  • G.F. Birkenmeier and F.K. Huang, Annihilator conditions on polynomials, Comm. Algebra 29(5) (2001), 2097-2112.
  • G.F. Birkenmeier and F.K. Huang, Annihilator conditions on formal power series, Algebra Colloq. 9(1) (2002), 29-37.
  • G.F. Birkenmeier, J. Y. Kim, J. Y. Park, Polynomial extensions of Baer and quasi-Baer rings, J. Pure and Appl. Algebra 159 (2001), 25-42.
  • G.F. Birkenmeier, J. Y. Kim, J. Y. Park, On quasi-Baer rings, Contemporery Mathematics, 259 (2000), 67-92.
  • G.F. Birkenmeier, H. E. Heatherly, J. Y. Kim, J. Y. Park, Triangular matrix representations, J. Algebra, 230 (2000), 558-595.
  • R. Camina, Subgroups of the Nottingham group, J. Algebra 196 (1997), 101
  • W.E. Clark, Twisted matrix units semigroup algebras, Duke Math. J. 34 (1967), 424.
  • S.A. Jennings, Substutution group of formal power series, Canad. J. Math. 6 (1954), 325-340.
  • D.L. Johnson, The group of formal power series under substitution, J. Austral. Math. Soc. 45 (1988), 296-302.
  • E. Hashemi and A. Moussavi, Polynomial extensions of quasi-Baer rings, Acta Math. Hungar. 107(3) (2005), 207-224.
  • E. Hashemi and A. Moussavi, Skew power series extensions of α-rigid p.p.- rings, Bull. Korean Math. Soc. 41(4) (2004), 657-665.
  • Y. Hirano, On annihilator ideals of a polynomial ring over a noncommutative rings, J. Pure Appl. Algebra, 168 (2002), 45-52.
  • C.Y. Hong, Nam Kyun Kim, Tai Keun Kwak, Ore extensions of Baer and p.p.-rings, J. Pure Appl. Algebra 151 (2000), 215-226.
  • I. Kaplansky, Rings of Operators, Benjamin, New York, 1965.
  • H. Lausch, W. Nobaure, Algebra of polynomials, Amsterdam: North Holland, (1973).
  • C.E. Rickart, Banach algebras with an adjoint operation, Ann. Math. 47 (1946), 658. Ebrahim Hashemi
  • Department of Mathematics Shahrood University of Technology Shahrood, Iran P.O.Box: 316-3619995161 e-mail: eb−hashemi@yahoo.com eb−hashemi@shahroodut.ac.ir

Year 2009, Volume: 6 Issue: 6, 38 - 45, 01.12.2009

Ebrahim Hashemi

Abstract

References

  • E.P. Armendariz, A note on extensions of Baer and p.p.-rings, J. Austral. Math. Soc. 18 (1974), 470-473.
  • S.K. Berberian, Baer *-rings, Springer-Verlag, Berlin, 1968.
  • G.F. Birkenmeier and F.K. Huang, Annihilator conditions on polynomials, Comm. Algebra 29(5) (2001), 2097-2112.
  • G.F. Birkenmeier and F.K. Huang, Annihilator conditions on formal power series, Algebra Colloq. 9(1) (2002), 29-37.
  • G.F. Birkenmeier, J. Y. Kim, J. Y. Park, Polynomial extensions of Baer and quasi-Baer rings, J. Pure and Appl. Algebra 159 (2001), 25-42.
  • G.F. Birkenmeier, J. Y. Kim, J. Y. Park, On quasi-Baer rings, Contemporery Mathematics, 259 (2000), 67-92.
  • G.F. Birkenmeier, H. E. Heatherly, J. Y. Kim, J. Y. Park, Triangular matrix representations, J. Algebra, 230 (2000), 558-595.
  • R. Camina, Subgroups of the Nottingham group, J. Algebra 196 (1997), 101
  • W.E. Clark, Twisted matrix units semigroup algebras, Duke Math. J. 34 (1967), 424.
  • S.A. Jennings, Substutution group of formal power series, Canad. J. Math. 6 (1954), 325-340.
  • D.L. Johnson, The group of formal power series under substitution, J. Austral. Math. Soc. 45 (1988), 296-302.
  • E. Hashemi and A. Moussavi, Polynomial extensions of quasi-Baer rings, Acta Math. Hungar. 107(3) (2005), 207-224.
  • E. Hashemi and A. Moussavi, Skew power series extensions of α-rigid p.p.- rings, Bull. Korean Math. Soc. 41(4) (2004), 657-665.
  • Y. Hirano, On annihilator ideals of a polynomial ring over a noncommutative rings, J. Pure Appl. Algebra, 168 (2002), 45-52.
  • C.Y. Hong, Nam Kyun Kim, Tai Keun Kwak, Ore extensions of Baer and p.p.-rings, J. Pure Appl. Algebra 151 (2000), 215-226.
  • I. Kaplansky, Rings of Operators, Benjamin, New York, 1965.
  • H. Lausch, W. Nobaure, Algebra of polynomials, Amsterdam: North Holland, (1973).
  • C.E. Rickart, Banach algebras with an adjoint operation, Ann. Math. 47 (1946), 658. Ebrahim Hashemi
  • Department of Mathematics Shahrood University of Technology Shahrood, Iran P.O.Box: 316-3619995161 e-mail: eb−hashemi@yahoo.com eb−hashemi@shahroodut.ac.ir
There are 19 citations in total.

Details

Other ID JA45YJ99YF
Journal Section Articles
Authors

Ebrahim Hashemi This is me

Publication Date December 1, 2009
Published in Issue Year 2009 Volume: 6 Issue: 6

Cite

APA Hashemi, E. (2009). DIFFERENTIAL POLYNOMIALS OVER BAER RINGS. International Electronic Journal of Algebra, 6(6), 38-45.
AMA Hashemi E. DIFFERENTIAL POLYNOMIALS OVER BAER RINGS. IEJA. December 2009;6(6):38-45.
Chicago Hashemi, Ebrahim. “DIFFERENTIAL POLYNOMIALS OVER BAER RINGS”. International Electronic Journal of Algebra 6, no. 6 (December 2009): 38-45.
EndNote Hashemi E (December 1, 2009) DIFFERENTIAL POLYNOMIALS OVER BAER RINGS. International Electronic Journal of Algebra 6 6 38–45.
IEEE E. Hashemi, “DIFFERENTIAL POLYNOMIALS OVER BAER RINGS”, IEJA, vol. 6, no. 6, pp. 38–45, 2009.
ISNAD Hashemi, Ebrahim. “DIFFERENTIAL POLYNOMIALS OVER BAER RINGS”. International Electronic Journal of Algebra 6/6 (December 2009), 38-45.
JAMA Hashemi E. DIFFERENTIAL POLYNOMIALS OVER BAER RINGS. IEJA. 2009;6:38–45.
MLA Hashemi, Ebrahim. “DIFFERENTIAL POLYNOMIALS OVER BAER RINGS”. International Electronic Journal of Algebra, vol. 6, no. 6, 2009, pp. 38-45.
Vancouver Hashemi E. DIFFERENTIAL POLYNOMIALS OVER BAER RINGS. IEJA. 2009;6(6):38-45.