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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

Yıl 2017, , 133 - 146, 11.07.2017

Ryan Gipson Hamid Kulosman

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

Öz

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 $M$.
 

Anahtar Kelimeler

Semigroup ring atomic domain

Kaynakça

  • 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.

Yıl 2017, , 133 - 146, 11.07.2017

Ryan Gipson Hamid Kulosman

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

Öz

Kaynakça

  • 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.
Toplam 4 adet kaynakça vardır.

Ayrıntılar

Konular Matematik
Bölüm Makaleler
Yazarlar

Ryan Gipson Bu kişi benim

Hamid Kulosman Bu kişi benim

Yayımlanma Tarihi 11 Temmuz 2017
Yayımlandığı Sayı Yıl 2017

Kaynak Göster

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. Temmuz 2017;22(22):133-146. doi:10.24330/ieja.325939
Chicago Gipson, Ryan, ve 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, sy. 22 (Temmuz 2017): 133-46. https://doi.org/10.24330/ieja.325939.
EndNote Gipson R, Kulosman H (01 Temmuz 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 ve H. Kulosman, “Atomic and AP semigroup rings $F[X;M]$, where $M$ is a submonoid of the additive monoid of nonnegative rational numbers”, IEJA, c. 22, sy. 22, ss. 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 (Temmuz 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 ve 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, c. 22, sy. 22, 2017, ss. 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.