Research Article
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Year 2018, , 50 - 61, 05.07.2018
https://doi.org/10.24330/ieja.440192

Abstract

References

  • N. Bourbaki, Algebra II, Chapters 4-7, Springer-Verlag, Berlin-Heidelberg, 2003.
  • 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.
  • N. J. Fine, Binomial coecients modulo a prime, Amer. Math. Monthly, 54 (1947), 589-592.
  • L. Fuchs, In nite Abelian Groups, Vol. II, Pure and Applied Mathematics, Vol. 36-II, Academic Press, New York-London, 1973.
  • R. Gilmer, Commutative Semigroup Rings, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1984.
  • R. Gilmer, Property E in commutative monoid rings, Group and semigroup rings (Johannesburg, 1985), North-Holland Math. Stud., 126, Notas Mat., 111, North-Holland, Amsterdam, (1986), 13-18.
  • 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, Int. Electron. J. Algebra, 22 (2017), 133-146.
  • T. Y. Lam and K. H. Leung, On vanishing sums of roots of unity, J. Algebra, 224(1) (2000), 91-109.
  • R. Matsuda, On algebraic properties of in nite group rings, Bull. Fac. Sci. Ibaraki Univ. Ser. A, 7 (1975), 29-37.
  • D. G. Northcott, Lessons on Rings, Modules and Multiplicities, Cambridge University Press, London, 1968.

IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS

Year 2018, , 50 - 61, 05.07.2018
https://doi.org/10.24330/ieja.440192

Abstract

We extend a lemma by Matsuda about the irreducibility of the
binomial X 􀀀 1 in the semigroup ring F[X;G], where F is a eld, G is an
abelian torsion-free group and is an element of G of height (0; 0; 0; : : : ).
In our extension, G is replaced by any submonoid of (Q+; +). The eld F,
however, has to be of characteristic 0. We give an application of our main
result.

References

  • N. Bourbaki, Algebra II, Chapters 4-7, Springer-Verlag, Berlin-Heidelberg, 2003.
  • 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.
  • N. J. Fine, Binomial coecients modulo a prime, Amer. Math. Monthly, 54 (1947), 589-592.
  • L. Fuchs, In nite Abelian Groups, Vol. II, Pure and Applied Mathematics, Vol. 36-II, Academic Press, New York-London, 1973.
  • R. Gilmer, Commutative Semigroup Rings, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1984.
  • R. Gilmer, Property E in commutative monoid rings, Group and semigroup rings (Johannesburg, 1985), North-Holland Math. Stud., 126, Notas Mat., 111, North-Holland, Amsterdam, (1986), 13-18.
  • 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, Int. Electron. J. Algebra, 22 (2017), 133-146.
  • T. Y. Lam and K. H. Leung, On vanishing sums of roots of unity, J. Algebra, 224(1) (2000), 91-109.
  • R. Matsuda, On algebraic properties of in nite group rings, Bull. Fac. Sci. Ibaraki Univ. Ser. A, 7 (1975), 29-37.
  • D. G. Northcott, Lessons on Rings, Modules and Multiplicities, Cambridge University Press, London, 1968.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Katie Christensen This is me

Ryan Gipson This is me

Hamid Kulosman This is me

Publication Date July 5, 2018
Published in Issue Year 2018

Cite

APA Christensen, K., Gipson, R., & Kulosman, H. (2018). IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS. International Electronic Journal of Algebra, 24(24), 50-61. https://doi.org/10.24330/ieja.440192
AMA Christensen K, Gipson R, Kulosman H. IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS. IEJA. July 2018;24(24):50-61. doi:10.24330/ieja.440192
Chicago Christensen, Katie, Ryan Gipson, and Hamid Kulosman. “IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS”. International Electronic Journal of Algebra 24, no. 24 (July 2018): 50-61. https://doi.org/10.24330/ieja.440192.
EndNote Christensen K, Gipson R, Kulosman H (July 1, 2018) IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS. International Electronic Journal of Algebra 24 24 50–61.
IEEE K. Christensen, R. Gipson, and H. Kulosman, “IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS”, IEJA, vol. 24, no. 24, pp. 50–61, 2018, doi: 10.24330/ieja.440192.
ISNAD Christensen, Katie et al. “IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS”. International Electronic Journal of Algebra 24/24 (July 2018), 50-61. https://doi.org/10.24330/ieja.440192.
JAMA Christensen K, Gipson R, Kulosman H. IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS. IEJA. 2018;24:50–61.
MLA Christensen, Katie et al. “IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS”. International Electronic Journal of Algebra, vol. 24, no. 24, 2018, pp. 50-61, doi:10.24330/ieja.440192.
Vancouver Christensen K, Gipson R, Kulosman H. IRREDUCIBILITY OF CERTAIN BINOMIALS IN SEMIGROUP RINGS FOR NONNEGATIVE RATIONAL MONOIDS. IEJA. 2018;24(24):50-61.