[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j180698

ANNIHILATING CONTENT IN POLYNOMIAL AND POWER SERIES RINGS

Abuosba, Emad (Department of Mathematics School of Science The University of Jordan)
Ghanem, Manal (Department of Mathematics School of Science The University of Jordan)

Publication Information

Journal of the Korean Mathematical Society / v.56, no.5, 2019 , pp. 1403-1418 More about this Journal

Abstract

Let R be a commutative ring with unity. If f(x) is a zero-divisor polynomial such that $$f(x)=c$ $_f f_1(x)$$ with $c_f{\in}R$ and $f_1(x)$ is not zero-divisor, then $c_f$ is called an annihilating content for f(x). In this case $Ann(f)=Ann(c_f )$ . We defined EM-rings to be rings with every zero-divisor polynomial having annihilating content. We showed that the class of EM-rings includes integral domains, principal ideal rings, and PP-rings, while it is included in Armendariz rings, and rings having a.c. condition. Some properties of EM-rings are studied and the zero-divisor graphs ${\Gamma}(R)$ and $${\Gamma}(R[x$ $]$ $)$$ are related if R was an EM-ring. Some properties of annihilating contents for polynomials are extended to formal power series rings.

Keywords

polynomial ring; power series ring; annihilating content; EM-ring; generalized morphic ring; zero-divisor graph;

Citations & Related Records

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