Presentations of a numerical semigroup
DOI:
https://doi.org/10.14419/gjma.v8i1.30464Keywords:
Catenary Degree, Complete Intersection, Connectedness, Minimal Presentations, Numerical Semigroups.Abstract
In this paper, we mainly study the minimal presentations of numerical semigroups. Moreover, we examine the concept of gluing, complete intersection, catenary degree, elasticity of some numerical semigroups.
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References
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[13] (Assi ve Garcia-Sanchez, 2014; Chapman ve ark., 2016; O’Neil ve ark., 2016).
[1]Rosales,J.C., Garcia-Sanches,P.A.,Numerical Semigroups,Springer,New York,2009.
[2]Abdallah, A., Garcia-Sanches, P.A.,Numerical Semigroups and Applications, Springer,Switzerland,2016.
[3]Omidali, M., Rahmati,F.,On the type and the minimal presentation of certain numerical semigroups,Communications in Algebra,37,4,(2009),1275-1283.
[4] Herzog,J.,Generators and relations of abelian semigroups and semigroups rings,Manuscripta Mathematica,3,2,(1970),175-193.
[5] Kunz,E.,The Value-Semigroup of a One-Dimensional Gorenstein Ring,Proceedings of the American Mathematical Society,25,4,(1970),748-751.
[6]Rosales,J.C., Garcia-Sanches,P.A., Numerical Semigroups(Developments in Mathematics),Springer, New York,2009.
[7] V.Barucci, Valentina Numerical semigroup algebras, in Multiplicative ideal theory in commutative algebra, 39-53, Springer,New York,2006.
[8] V.Barucci, D.E. Dobbs, M.Fontana, Maximality Properties in Numerical Semigroups and Applications to One-Dimensional Analytically Irreducible Local Domains, Memoirs of the Amer. Math. Soc. 598 (1997).
[9] L.Redei, The theory of finitely generated commutative semigroups, Pergamon, Oxford-Edinburgh-New York, 1965.
[10] P. Freyd, Redei’s finiteness theorem for commutative semigroups, Proc. Amer. Math. Soc. 19 (1968), 1003.
[11] P.A. Grillet, A short proof of Redei’s theorem, Semigroup Forum, Semigroup Forum 46 (1993), 126-127.
[12] J. Herzog, Generators and relations of abelian semigroups and semigroup rings, Manuscripta Math. 3 (1970), 175-193.
[13] J. C. Rosales, Function minimum associated to a congruence on integral n-tuple space, Semigroup Forum 51 (1995) 87-95.
[14] J. C. Rosales, P.A. Garcia-Sanches, J.M. Urbano-Blanco, On presentations of commutative monoids, Internat. J. Algebra Comput. 9 (1999), no. 5, 539-553.
[15] J. C. Rosales, Semigrupos numericos, Tesis Doctoral, Universidad de Granada, Spain, 2001.
[16] J. C. Rosales, An algorithmic method to compute a minimal relation for any numerical semigroup, Internat. J. Algebra Comput. 6 (1996), no. 4, 441-455.
[17] H. Bresinsky, On prime ideals with generic zeo , Proc. Amer. Math. Soc. 47 (1975), 329-332.
[18] D. Narsingh, Graph Theory with Applications to Engineering and Computer Science, Prentice Hall Series in Automatic Computation, 1974.
[19] (Assi ve Garcia-Sanchez, 2014; Chapman ve ark., 2016; O’Neil ve ark., 2016).
[20] (Assi ve Garcia-Sanchez, 2014; Chapman ve ark., 2016; O’Neil ve ark., 2016).
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