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

Year 2017, Volume: 22 Issue: 22, 133 - 146, 11.07.2017

Ryan Gipson Hamid Kulosman

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

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.

Year 2017, Volume: 22 Issue: 22, 133 - 146, 11.07.2017

Ryan Gipson Hamid Kulosman

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

Abstract

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.
There are 4 citations in total.

Details

Subjects Mathematical Sciences
Journal Section Articles
Authors

Ryan Gipson This is me

Hamid Kulosman This is me

Publication Date July 11, 2017
Published in Issue Year 2017 Volume: 22 Issue: 22

Cite

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 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. July 2017;22(22):133-146. doi:10.24330/ieja.325939
Chicago 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 22, no. 22 (July 2017): 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 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, 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 2017), 133-146. https://doi.org/10.24330/ieja.325939.
JAMA 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, 2017, pp. 133-46, doi:10.24330/ieja.325939.
Vancouver 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):133-46.