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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
https://izlik.org/JA97GL34BR

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
https://izlik.org/JA97GL34BR

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 Research Article
Authors

Ryan Gipson This is me

Hamid Kulosman This is me

Publication Date July 11, 2017
DOI https://doi.org/10.24330/ieja.325939
IZ https://izlik.org/JA97GL34BR
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 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