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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, Cilt: 22 Sayı: 22, 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, Cilt: 22 Sayı: 22, 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 Cilt: 22 Sayı: 22

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.