DEGREES OF SOLID VARIETIES OF SEMIRINGS

For any arbitrary variety V , the degree dp(V ) of V with respectto proper hypersubstitutions was introduced in [6]. This degree of any varietyof bands was determined in [4]. In this paper we characterize the universe ofthe free algebra of each solid variety of semirings and from this we derive thedegree dp(V ) if V is any solid variety of semirings.

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  • [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).