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Gömme Boyutu Üç Olan Bazı Pseudo-Simetrik Sayısal Yarıgruplarının Delta Kümeleri Üzerine

Year 2022, , 335 - 343, 24.03.2022
https://doi.org/10.17798/bitlisfen.1024066

Abstract

S bir sayısal yarıgrup olsun. S deki bir s elemanın katener derecesi, s 'nin çarpanlara ayırmaları arasındaki mesafeyi ölçmek için kullanılan negatif olmayan bir tamsayıdır. S sayısal yarıgurubunun katener derecesi, elemanlarının maksimum katener derecesinde elde edilir. S'nin maksimum katener derecesine, S'nin karmaşık özelliklere sahip Betti elemanları ile ulaşılır. S'nin Betti elemanları, S'nin tüm minimal gösterimlerinden elde edilebilir. S için bir gösterim, özel çarpan homomorfizminin çekirdek kongrüansının üreteçlerinden oluşan bir sistemdir. Eğer bir gösterim başka bir gösterime dönüştürülemiyorsa, yani onun herhangi bir öz alt kümesi bir gösterim değil ise, minimaldir. S'nin Delta kümesi, S'deki elemanlar için çarpanlarının uzunluklarının kümelerinin karmaşıklığını ölçen bir çarpan değişmezidir.
Bu çalışmada, özel bir pseudo-simetrik sayısal yarı grup ailesinin yukarıdaki değişmezlerini onun üreteçleri açısından ifade edeceğiz.

References

  • Assi, A., García-Sánchez, P.A. 2016. Numerical semigroups and applications. Cham: RSME Springer Series, Springer, pp. 106.
  • Chapman S.T., García-Sánchez P.A, Tripp Z., Viola, C. 2016. Measuring primality in numerical semigroups with embedding dimension three. Journal of Algebra and Its Applications, 15(1): pp. 16.
  • Chapman S.T., Hoyer R., Kaplan N. 2009. Delta Sets of Numerical Monoids are Eventually Periodic. Aequationes Math., 77: 273-279.
  • Chapman S.T., Kaplan N., Daigle J., Hoyer R. 2010. Delta Sets of Numerical Monoids Using Non-Minimal Sets of Generators. Comm. Algebra, 38: 2622-2634.
  • Chapman S.T., Kaplan N., Lemburg T., Niles A., Zlogar C. 2014. Shifts of Generators and Delta Sets of Numerical Monoids. Internat. J. Algebra Comp., 24(5): 655–669.
  • Conaway R., Gotti F., Horton J., O’Neill C., Pelayo R., Williams M., Wissman B. 2018. Minimal presentations of shifted numerical monoids. International Journal of Algebra and Computation, 28(1): 53–68.
  • Conaway R., Williams M., Horton J., Gotti F. 2015. Shifting numerical semigroups. Allen Institute for Artificial Intelligence. https://www.semanticscholar.org. (Date of access: 5.12. 2020).
  • Delgado M., García-Sánchez P.A., Morais J. 2020. “numericalsgps”: a gap package on numerical semigroups. https://www.gap-system.org/Packages/numericalsgps.html. (Date of access: 11.11 2021).
  • García-Sánchez P.A., Llena D., Moscariello A. 2015. Delta sets for numerical semigroups with embedding dimension three. https://arxiv.org/abs/1504.02116v1 (Date of access: 11.11.2021).
  • Geroldinger A. 1991. On the arithmetic of certain not integrally closed Noetherian integral domains. Comm. Algebra, 19: 685–698.
  • Geroldinger A., Halter-Koch F. 2006. Non-unique factorizations: Algebraic, combinatorial and analytic theory, Pure and Applied Mathematics, Chapman and Hall/CRC, 1st edition. Boca Raton- London-New York, pp. 728.
  • Narsingh D. 1974. Graph Theory with Applications to Engineering and Computer Science. USA: Prentice Hall Series in Automatic Computation. The United States of America, pp. 478.
  • O’Neil C., Ponomorenko V., Tate R., Webb G. 2016. On the set of catenary degrees of finitely generated cancellative commutative monoids. International Journal of Algebra and Computation, 26(3): 565-576.
  • Rosales J.C., Branco M.B. 2003. Irreducible numerical semigroups with arbitrary multiplicity and embedding dimension. J. Algebra, 264: 305–315.
  • Rosales J.C., García-Sánchez P.A. 1999. Finitely generated commutative monoids. Nova 28 Science Publishers, New York, pp. 185.
  • Rosales J.C., García-Sánchez P.A. 2009. Numerical semigroups. In: Developments in Mathematics. Springer, vol. 20, New York, pp. 181.
  • Schwartz M.S. 2019. Factorization Lengths in Numerical Monoids. https://digitalcommons.bard.edu/cgi/viewcontent.cgi?article=1034&context=senproj_s2019 (Date of access: 11.11. 2021).

On Delta Sets Of Some Pseudo-Symmetric Numerical Semigroups With Embedding Dimension Three

Year 2022, , 335 - 343, 24.03.2022
https://doi.org/10.17798/bitlisfen.1024066

Abstract

Let S be a numerical semigroup. The catenary degree of an element s in S is a non-negative integer used to measure the distance between factorizations of s. The catenary degree of the numerical semigroup S is obtained at the maximum catenary degree of its elements. The maximum catenary degree of S is attained via Betti elements of S with complex properties. The Betti elements of S can be obtained from all minimal presentations of S. A presentation for S is a system of generators of the kernel congruence of the special factorization homomorphism. A presentation is minimal if it can not be converted to another presentation, that is, any of its proper subsets is no longer a presentation. The Delta set of S is a factorization invariant measuring the complexity of sets of the factorization lengths for the elements in S.
In this study, we will mainly express the given above invariants of a special pseudo-symmetric numerical semigroup family in terms of its generators.

References

  • Assi, A., García-Sánchez, P.A. 2016. Numerical semigroups and applications. Cham: RSME Springer Series, Springer, pp. 106.
  • Chapman S.T., García-Sánchez P.A, Tripp Z., Viola, C. 2016. Measuring primality in numerical semigroups with embedding dimension three. Journal of Algebra and Its Applications, 15(1): pp. 16.
  • Chapman S.T., Hoyer R., Kaplan N. 2009. Delta Sets of Numerical Monoids are Eventually Periodic. Aequationes Math., 77: 273-279.
  • Chapman S.T., Kaplan N., Daigle J., Hoyer R. 2010. Delta Sets of Numerical Monoids Using Non-Minimal Sets of Generators. Comm. Algebra, 38: 2622-2634.
  • Chapman S.T., Kaplan N., Lemburg T., Niles A., Zlogar C. 2014. Shifts of Generators and Delta Sets of Numerical Monoids. Internat. J. Algebra Comp., 24(5): 655–669.
  • Conaway R., Gotti F., Horton J., O’Neill C., Pelayo R., Williams M., Wissman B. 2018. Minimal presentations of shifted numerical monoids. International Journal of Algebra and Computation, 28(1): 53–68.
  • Conaway R., Williams M., Horton J., Gotti F. 2015. Shifting numerical semigroups. Allen Institute for Artificial Intelligence. https://www.semanticscholar.org. (Date of access: 5.12. 2020).
  • Delgado M., García-Sánchez P.A., Morais J. 2020. “numericalsgps”: a gap package on numerical semigroups. https://www.gap-system.org/Packages/numericalsgps.html. (Date of access: 11.11 2021).
  • García-Sánchez P.A., Llena D., Moscariello A. 2015. Delta sets for numerical semigroups with embedding dimension three. https://arxiv.org/abs/1504.02116v1 (Date of access: 11.11.2021).
  • Geroldinger A. 1991. On the arithmetic of certain not integrally closed Noetherian integral domains. Comm. Algebra, 19: 685–698.
  • Geroldinger A., Halter-Koch F. 2006. Non-unique factorizations: Algebraic, combinatorial and analytic theory, Pure and Applied Mathematics, Chapman and Hall/CRC, 1st edition. Boca Raton- London-New York, pp. 728.
  • Narsingh D. 1974. Graph Theory with Applications to Engineering and Computer Science. USA: Prentice Hall Series in Automatic Computation. The United States of America, pp. 478.
  • O’Neil C., Ponomorenko V., Tate R., Webb G. 2016. On the set of catenary degrees of finitely generated cancellative commutative monoids. International Journal of Algebra and Computation, 26(3): 565-576.
  • Rosales J.C., Branco M.B. 2003. Irreducible numerical semigroups with arbitrary multiplicity and embedding dimension. J. Algebra, 264: 305–315.
  • Rosales J.C., García-Sánchez P.A. 1999. Finitely generated commutative monoids. Nova 28 Science Publishers, New York, pp. 185.
  • Rosales J.C., García-Sánchez P.A. 2009. Numerical semigroups. In: Developments in Mathematics. Springer, vol. 20, New York, pp. 181.
  • Schwartz M.S. 2019. Factorization Lengths in Numerical Monoids. https://digitalcommons.bard.edu/cgi/viewcontent.cgi?article=1034&context=senproj_s2019 (Date of access: 11.11. 2021).
There are 17 citations in total.

Details

Primary Language English
Journal Section Araştırma Makalesi
Authors

Meral Süer 0000-0002-5512-4305

Özkan Çelik 0000-0002-1570-6060

Publication Date March 24, 2022
Submission Date November 15, 2021
Acceptance Date February 22, 2022
Published in Issue Year 2022

Cite

IEEE M. Süer and Ö. Çelik, “On Delta Sets Of Some Pseudo-Symmetric Numerical Semigroups With Embedding Dimension Three”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 11, no. 1, pp. 335–343, 2022, doi: 10.17798/bitlisfen.1024066.



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