DEGREES OF SOLID VARIETIES OF SEMIRINGS

Hippolyte Hounnon; Klaus Denecke

doi:10.36753/mathenot.421193

EN

DEGREES OF SOLID VARIETIES OF SEMIRINGS

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.

Keywords

Semiring,hypersubstitution,hyperidentity,solid variety

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).

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

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 Number: 1

DOI

https://doi.org/10.36753/mathenot.421193

IZ

https://izlik.org/JA66DR34HD

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

1.Hounnon H, Denecke K. DEGREES OF SOLID VARIETIES OF SEMIRINGS. Math. Sci. Appl. E-Notes. 2015;3(1):1-12. doi:10.36753/mathenot.421193

Chicago

Hounnon, Hippolyte, and Klaus Denecke. 2015. “DEGREES OF SOLID VARIETIES OF SEMIRINGS”. Mathematical Sciences and Applications E-Notes 3 (1): 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

[1]H. Hounnon and K. Denecke, “DEGREES OF SOLID VARIETIES OF SEMIRINGS”, Math. Sci. Appl. E-Notes, vol. 3, no. 1, pp. 1–12, May 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 1, 2015): 1-12. https://doi.org/10.36753/mathenot.421193.

JAMA

1.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, May 2015, pp. 1-12, doi:10.36753/mathenot.421193.

Vancouver

1.Hippolyte Hounnon, Klaus Denecke. DEGREES OF SOLID VARIETIES OF SEMIRINGS. Math. Sci. Appl. E-Notes. 2015 May 1;3(1):1-12. doi:10.36753/mathenot.421193