Presentations of a numerical semigroup

 
 
 
  • Abstract
  • Keywords
  • References
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  • 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.

     

     


  • Keywords


    Catenary Degree; Complete Intersection; Connectedness; Minimal Presentations; Numerical Semigroups.

  • References


      [1] V. Barucci, Valentina Numerical semigroup algebras, in Multiplicative ideal theory in commutative algebra, 39-53, Springer, New York, 2006. “available online : https://doi.org/10.1007/978-0-387-36717-0_3.

      [2] 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). “available online : https://doi.org/10.1090/memo/0598.

      [3] L. Redei, The theory of finitely generated commutative semigroups, Pergamon, Oxford-Edinburgh-New York, 1965.

      [4] P. Freyd, Redei’s finiteness theorem for commutative semigroups, Proc. Amer. Math. Soc. 19 (1968), 1003. “available online : https://doi.org/10.1090/S0002-9939-1968-0227290-4.

      [5] P. A. Grillet, A short proof of Redei’s theorem, Semigroup Forum 46 (1993), 126-127.”available online : https://doi.org/10.1007/BF02573555.

      [6] J. Herzog, Generators and relations of abelian semigroups and semigroup rings, Manuscripta Math. 3 (1970), 175-193. “available online : https://doi.org/10.1007/BF01273309.

      [7] J. C. Rosales, Function minimum associated to a congruence on integral n-tuple space, Semigroup Forum 51 (1995) 87-95. “available online : https://doi.org/10.1007/BF02573622.

      [8] 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. “available online : https://doi.org/10.1142/S0218196799000333.

      [9] J. C. Rosales, Semigrupos numericos, Tesis Doctoral, Universidad de Granada, Spain, 2001.

      [10] 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.” available online : https://doi.org/10.1142/S021819679600026X.

      [11] H. Bresinsky, On prime ideals with generic zeo , Proc. Amer. Math. Soc. 47 (1975), 329-332. “available online : https://doi.org/10.2307/2039739.

      [12] D. Narsingh, Graph Theory with Applications to Engineering and Computer Science, Prentice Hall Series in Automatic Computation, 1974.

      [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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Article ID: 30464
 
DOI: 10.14419/gjma.v8i1.30464




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