Atomic and AP semigroup rings $F[X;M]$, where $M$ is a submonoid of the additive monoid of nonnegative rational numbers

Ryan Gipson; Hamid Kulosman

doi:10.24330/ieja.325939

EN

Atomic and AP semigroup rings $F[X;M]$, where $M$ is a submonoid of the additive monoid of nonnegative rational numbers

Abstract

We investigate the atomicity and the AP property of the semigroup rings $F[X;M]$, where $F$ is a field, $X$ is a variable and $M$ is a submonoid of the additive monoid of nonnegative rational numbers. The main notion that we introduce for the purpose of the investigation is the notion of essential generators of $M$.

Keywords

Semigroup ring,atomic domain

References

P. J. Allen and L. Dale, Ideal theory in the semiring Z+, Publ. Math. Debrecen, 22 (1975), 219-224.
D. D. Anderson, D. F. Anderson and M. Zafrullah, Factorization in integral domains, J. Pure Appl. Algebra, 69(1) (1990), 1-19.
R. C. Daileda, A non-UFD integral domains in which irreducibles are prime, preprint. http://ramanujan.math.trinity.edu/rdaileda/teach/m4363s07/non_ufd.pdf.
R. Gilmer, Commutative Semigroup Rings, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1984.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Ryan Gipson This is me

Hamid Kulosman This is me

Publication Date

July 11, 2017

Submission Date

July 4, 2017

Acceptance Date

-

Published in Issue

Year 2017 Volume: 22 Number: 22

DOI

https://doi.org/10.24330/ieja.325939

IZ

https://izlik.org/JA97GL34BR

Cite

RIS / Bibtex

APA

Gipson, R., & Kulosman, H. (2017). Atomic and AP semigroup rings $F[X;M]$, where $M$ is a submonoid of the additive monoid of nonnegative rational numbers. International Electronic Journal of Algebra, 22(22), 133-146. https://doi.org/10.24330/ieja.325939

AMA

1.Gipson R, Kulosman H. Atomic and AP semigroup rings $F[X;M]$, where $M$ is a submonoid of the additive monoid of nonnegative rational numbers. IEJA. 2017;22(22):133-146. doi:10.24330/ieja.325939

Chicago

Gipson, Ryan, and Hamid Kulosman. 2017. “Atomic and AP Semigroup Rings $F[X;M]$, Where $M$ Is a Submonoid of the Additive Monoid of Nonnegative Rational Numbers”. International Electronic Journal of Algebra 22 (22): 133-46. https://doi.org/10.24330/ieja.325939.

EndNote

Gipson R, Kulosman H (July 1, 2017) Atomic and AP semigroup rings $F[X;M]$, where $M$ is a submonoid of the additive monoid of nonnegative rational numbers. International Electronic Journal of Algebra 22 22 133–146.

IEEE

[1]R. Gipson and H. Kulosman, “Atomic and AP semigroup rings $F[X;M]$, where $M$ is a submonoid of the additive monoid of nonnegative rational numbers”, IEJA, vol. 22, no. 22, pp. 133–146, July 2017, doi: 10.24330/ieja.325939.

ISNAD

Gipson, Ryan - Kulosman, Hamid. “Atomic and AP Semigroup Rings $F[X;M]$, Where $M$ Is a Submonoid of the Additive Monoid of Nonnegative Rational Numbers”. International Electronic Journal of Algebra 22/22 (July 1, 2017): 133-146. https://doi.org/10.24330/ieja.325939.

JAMA

1.Gipson R, Kulosman H. Atomic and AP semigroup rings $F[X;M]$, where $M$ is a submonoid of the additive monoid of nonnegative rational numbers. IEJA. 2017;22:133–146.

MLA

Gipson, Ryan, and Hamid Kulosman. “Atomic and AP Semigroup Rings $F[X;M]$, Where $M$ Is a Submonoid of the Additive Monoid of Nonnegative Rational Numbers”. International Electronic Journal of Algebra, vol. 22, no. 22, July 2017, pp. 133-46, doi:10.24330/ieja.325939.

Vancouver

1.Ryan Gipson, Hamid Kulosman. Atomic and AP semigroup rings $F[X;M]$, where $M$ is a submonoid of the additive monoid of nonnegative rational numbers. IEJA. 2017 Jul. 1;22(22):133-46. doi:10.24330/ieja.325939