Affiliation:
1. Department of Engineering Science , Golpayegan University of Technology , Golpayegan , Iran
Abstract
Abstract
We prove McCoy’s property for the zero-divisors of polynomials in semirings, investigate the zero-divisors of semimodules and prove that under suitable conditions, the monoid semimodule
M
[
G
]
{M[G]}
has very few zero-divisors if and only if the S-semimodule M does so.
The concept of Auslander semimodules is introduced as well.
Then we introduce Ohm–Rush and McCoy semialgebras and prove some interesting results for prime ideals of monoid semirings.
Finally, we investigate the set of zero-divisors of McCoy semialgebras.
We also introduce strong Krull primes for semirings and investigate their extension in semialgebras.
Reference40 articles.
1. S. Bourne,
The Jacobson radical of a semiring,
Proc. Natl. Acad. Sci. USA 37 (1951), 163–170.
2. W. Bruns and J. Gubeladze,
Polytopes, Rings, and K-theory,
Springer Monogr. Math.,
Springer, Dordrecht, 2009.
3. W. Bruns and J. Herzog,
Cohen–Macaulay Rings,
Cambridge Stud. Adv. Math. 39,
Cambridge University, Cambridge, 1993.
4. J. Dauns,
Primal modules,
Comm. Algebra 25 (1997), no. 8, 2409–2435.
5. E. D. Davis,
Overrings of commutative rings. II. Integrally closed overrings,
Trans. Amer. Math. Soc. 110 (1964), 196–212.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. $$I^\times C$$-Semirings;Bulletin of the Iranian Mathematical Society;2022-11-28
2. On generalized derivations of semirings;Georgian Mathematical Journal;2022-07-22
3. The McCoy property in Ohm–Rush algebras;Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry;2021-03-10