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Vietnam Journal of Mathematics 40:1 (2012)
47-55
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On Polynomials over Abelian Rings
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Ebrahim Hashemi1 and Ali Akbar
Estaji2
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1Department of Mathematics,
Shahrood University of Technology,
Shahrood, P. O. Box 316-3619995161, Iran
2Department of
Mathematics, Sabzevar Tarbiat Moallem University,
Sabzevar, P. O. Box 397, Iran
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Received March 27, 2011
Revised November 29, 2011
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Abstract. In this paper we study various
annihilator conditions over nearrings of polynomials and formal power
series over an abelian ring, which were originally used by Rickart and
Kaplansky to abstract the algebraic properties of von Neumann algebra.
These results are somewhat surprising since, in contrast to the polynomial
ring case, the nearrings of polynomials and formal power series have
substitution for its “multiplication” operation. As a consequence we obtain
a generalization of [10].
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2000 Mathematics
Subject Classification. 16Y30, 16Y99.
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Keywords. Baer
rings, quasi-Baer rings, reduced rings, IFP rings, nearring of polynomials,
formal power series.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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