The Journal of the Indian Mathematical Society

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A Remark on n-absorbing Ideals of Principal Ideal Domains


Affiliations
1 Department of Mathematics M. J. College, Jalgaon - 425 002, India
     

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Let R be a commutative ring with identity 1 ≠ 0. General-izing the notion of prime ideals in R, Anderson and Badawi introduced the notion of n-absorbing ideals in R. We introduce the notion of n- absorbing domains which is a generalization of an integral domain. We investigate all n-absorbing ideals in a PID R and hence prove that Zm is an n-absorbing domain if and only if m = p1r1 p2r2 p3r3 …pkrk where k ≤ n and r1 + r2 + r3 + … + rk ≤ n.

Keywords

Principal Ideal Domain, n-Absorbing Ideal, n-Absorbing Domain.
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  • D. F. Anderson and Ayman Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra 39(2011), 1646 – 1672.

  • Ayman Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. Vol. 75(2007), 417 – 429.

  • I. N. Herstein, Topics in algebra, Blaisdell Publishing company, 1964.

  • Sh. Payrovi and S. Babaei, On the 2-absorbing ideals in commutative rings, Bull.Malays. Math. Sci. Soc. (To appear).


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  • A Remark on n-absorbing Ideals of Principal Ideal Domains

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Authors

Jayprakash Ninu Chaudhari
Department of Mathematics M. J. College, Jalgaon - 425 002, India

Abstract


Let R be a commutative ring with identity 1 ≠ 0. General-izing the notion of prime ideals in R, Anderson and Badawi introduced the notion of n-absorbing ideals in R. We introduce the notion of n- absorbing domains which is a generalization of an integral domain. We investigate all n-absorbing ideals in a PID R and hence prove that Zm is an n-absorbing domain if and only if m = p1r1 p2r2 p3r3 …pkrk where k ≤ n and r1 + r2 + r3 + … + rk ≤ n.

Keywords


Principal Ideal Domain, n-Absorbing Ideal, n-Absorbing Domain.

References