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Year 2015, Volume: 3 Issue: 1, 1 - 12, 15.05.2015
https://doi.org/10.36753/mathenot.421193

Abstract

References

  • [1] Denecke, K., Hounnon, H., Solid Varieties of Normal ID-Semirings, General Algebra and Discrete Mathematics, Proceedings of the 59th Workshop on General Algebra, 15th Conference for Young Algebraists, Potsdam 2000, Shaker Verlag Aachen (2000), 25-40.
  • [2] Denecke, K., Hounnon, H., Solid Varieties of Semirings, Proceedings of the International Conferenc on Semigroups, Braga (Portugal) 1999, World Scientific (2000), 69-86.
  • [3] Denecke, K. and Hounnon, H., All solid varieties of semirings, Journal of Algebra 248 (2002), 107-117.
  • [4] Denecke, K., Koppitz, J., Srithus, K., N-fluid varieties, Scientiae Mathematicae Japonicae 65, No. 1 (2007), 1-19: e-2006, 1025-1034.
  • [5] Denecke, K. Koppitz, J., Srithus, K., The Degree of Proper Hypersubstitutions, Scientiae Mathematicae Japonicae Online e-2007, 301-314.
  • [6] Denecke, K., Srithus, K., Binary Relations on the Monoid of V -proper Hypersubstitutions, Discussiones Mathematicae, General Algebra and Applications 26 (2006), 233-251.
  • [7] Denecke, K., Wismath, S. L., Hyperidentities and Clones, Gordon and Breach Science Publishers (2000).
  • [8] Graczy´nska, E. On normal and regular identities and hyperidentities, Proceedings of the V Universal Algebra Symposium, Universal and Applied Algebra, Turawa, Poland, Word Scientific (1989), 107-135.
  • [9] Graczy´nska, E. and Schweigert, D. Hypervarieties of a given type, Algebra Universalis, 27 (1990), 305-31
  • [10] Hounnon, H., Hyperidentities in Semirings and Applications Shaker Verlag, Aachen (2002).
  • [11] P lonka, J., Proper and inner hypersubstitutions of varieties, Proceedings of the International Conference: Summer School on General Algebra and Ordered Sets, Palacky University Olomouc (1994), 106-115.
  • [12] R. McKenzie, G. McNulty and W.F. Taylor, Algebras, Lattices Varieties Vol 1, 1987 Inc. Belmonts Califormia.
  • [13] Srithus, R. Algebras Derived by Hypersubstitutions, PhD thesis, Potsdam University, Germany (2008).

DEGREES OF SOLID VARIETIES OF SEMIRINGS

Year 2015, Volume: 3 Issue: 1, 1 - 12, 15.05.2015
https://doi.org/10.36753/mathenot.421193

Abstract

For any arbitrary variety V , the degree dp(V ) of V with respect

to proper hypersubstitutions was introduced in [6]. This degree of any variety

of bands was determined in [4]. In this paper we characterize the universe of

the free algebra of each solid variety of semirings and from this we derive the

degree dp(V ) if V is any solid variety of semirings.

References

  • [1] Denecke, K., Hounnon, H., Solid Varieties of Normal ID-Semirings, General Algebra and Discrete Mathematics, Proceedings of the 59th Workshop on General Algebra, 15th Conference for Young Algebraists, Potsdam 2000, Shaker Verlag Aachen (2000), 25-40.
  • [2] Denecke, K., Hounnon, H., Solid Varieties of Semirings, Proceedings of the International Conferenc on Semigroups, Braga (Portugal) 1999, World Scientific (2000), 69-86.
  • [3] Denecke, K. and Hounnon, H., All solid varieties of semirings, Journal of Algebra 248 (2002), 107-117.
  • [4] Denecke, K., Koppitz, J., Srithus, K., N-fluid varieties, Scientiae Mathematicae Japonicae 65, No. 1 (2007), 1-19: e-2006, 1025-1034.
  • [5] Denecke, K. Koppitz, J., Srithus, K., The Degree of Proper Hypersubstitutions, Scientiae Mathematicae Japonicae Online e-2007, 301-314.
  • [6] Denecke, K., Srithus, K., Binary Relations on the Monoid of V -proper Hypersubstitutions, Discussiones Mathematicae, General Algebra and Applications 26 (2006), 233-251.
  • [7] Denecke, K., Wismath, S. L., Hyperidentities and Clones, Gordon and Breach Science Publishers (2000).
  • [8] Graczy´nska, E. On normal and regular identities and hyperidentities, Proceedings of the V Universal Algebra Symposium, Universal and Applied Algebra, Turawa, Poland, Word Scientific (1989), 107-135.
  • [9] Graczy´nska, E. and Schweigert, D. Hypervarieties of a given type, Algebra Universalis, 27 (1990), 305-31
  • [10] Hounnon, H., Hyperidentities in Semirings and Applications Shaker Verlag, Aachen (2002).
  • [11] P lonka, J., Proper and inner hypersubstitutions of varieties, Proceedings of the International Conference: Summer School on General Algebra and Ordered Sets, Palacky University Olomouc (1994), 106-115.
  • [12] R. McKenzie, G. McNulty and W.F. Taylor, Algebras, Lattices Varieties Vol 1, 1987 Inc. Belmonts Califormia.
  • [13] Srithus, R. Algebras Derived by Hypersubstitutions, PhD thesis, Potsdam University, Germany (2008).
There are 13 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Hippolyte Hounnon

Klaus Denecke This is me

Publication Date May 15, 2015
Submission Date May 13, 2013
Acceptance Date October 23, 2014
Published in Issue Year 2015 Volume: 3 Issue: 1

Cite

APA Hounnon, H., & Denecke, K. (2015). DEGREES OF SOLID VARIETIES OF SEMIRINGS. Mathematical Sciences and Applications E-Notes, 3(1), 1-12. https://doi.org/10.36753/mathenot.421193
AMA Hounnon H, Denecke K. DEGREES OF SOLID VARIETIES OF SEMIRINGS. Math. Sci. Appl. E-Notes. May 2015;3(1):1-12. doi:10.36753/mathenot.421193
Chicago Hounnon, Hippolyte, and Klaus Denecke. “DEGREES OF SOLID VARIETIES OF SEMIRINGS”. Mathematical Sciences and Applications E-Notes 3, no. 1 (May 2015): 1-12. https://doi.org/10.36753/mathenot.421193.
EndNote Hounnon H, Denecke K (May 1, 2015) DEGREES OF SOLID VARIETIES OF SEMIRINGS. Mathematical Sciences and Applications E-Notes 3 1 1–12.
IEEE H. Hounnon and K. Denecke, “DEGREES OF SOLID VARIETIES OF SEMIRINGS”, Math. Sci. Appl. E-Notes, vol. 3, no. 1, pp. 1–12, 2015, doi: 10.36753/mathenot.421193.
ISNAD Hounnon, Hippolyte - Denecke, Klaus. “DEGREES OF SOLID VARIETIES OF SEMIRINGS”. Mathematical Sciences and Applications E-Notes 3/1 (May 2015), 1-12. https://doi.org/10.36753/mathenot.421193.
JAMA Hounnon H, Denecke K. DEGREES OF SOLID VARIETIES OF SEMIRINGS. Math. Sci. Appl. E-Notes. 2015;3:1–12.
MLA Hounnon, Hippolyte and Klaus Denecke. “DEGREES OF SOLID VARIETIES OF SEMIRINGS”. Mathematical Sciences and Applications E-Notes, vol. 3, no. 1, 2015, pp. 1-12, doi:10.36753/mathenot.421193.
Vancouver Hounnon H, Denecke K. DEGREES OF SOLID VARIETIES OF SEMIRINGS. Math. Sci. Appl. E-Notes. 2015;3(1):1-12.

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