Ideal theory in graded semirings

Authors

P. J. Allen, Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U.S.A.
H. S. Kim
J. Neggers

Author Country (or Countries)

U.S.A.

Abstract

An A-semiring has commutative multiplication and the property that every proper ideal B is contained in a prime ideal P, with pB, the intersection of all such prime ideals. In this paper, we define homogeneous ideals and their radicals in a graded semiring R. When B is a proper homogeneous ideal in an A-semiring R, we show that pB is homogeneous whenever pB is a k-ideal.We also give necessary and sufficient conditions that a homogeneous k-ideal P be completely prime (i.e., F 62 P;G 62 P implies FG 62 P) in any graded semiring. Indeed, we may restrict F and G to be homogeneous elements of R.

Suggested Reviewers

N/A

Recommended Citation

J. Allen, P.; S. Kim, H.; and Neggers, J. (2013) "Ideal theory in graded semirings," Applied Mathematics & Information Sciences: Vol. 07: Iss. 1, Article 9.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss1/9