Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
hyperidentity; pre-hyperidentity; pre-solid variety
hyperidentity; pre-hyperidentity; pre-solid variety
Summary:
Pre-hyperidentities generalize the concept of a hyperidentity. A variety $V$ is said to be pre-solid if every identity in $V$ is a pre-hyperidentity. Every solid variety is pre-solid. We consider pre-solid varieties of semigroups which are not solid, determine the smallest and the largest of them, and some elements in this interval.
References:
[1] Denecke K., Koppitz J.: Hyperassociative semigroups. Semigroup Forum, Vol. 49,(1994) 41-48. MR 1272861
[2] Denecke K., Lau D., Pöschel R., Schweigert D.: Hyperidentities, hyperequational classes and clone congruences. Contributions to General Algebra 7, Verlag Hölder-Pichler-Tempsky, Wien 1991 - Verlag B.G. Teubner, Stuttgart (1991) 97-118. MR 1143072 | Zbl 0759.08005
[3] Denecke K., Wismath S. L.: Solid varieties of semigroups. Semigroup Forum, Vol. 48, (1994) 219-234. MR 1256690 | Zbl 0797.20045
[4] Denecke K., Płonka J.: On regularizations and normalizations of solid varieties. in: General Algebra and Discrete Mathematics, Berlin 1995, 83-92.
[5] Denecke K., Koppitz J.: Presolid varieties of commutative semigroups. preprint 1993. MR 1384792
[6] Denecke K., Lau D., Pöschel R., Schweigert D.: Free Clones and Solid Varieties. preprint 1993. MR 1336152
[7] Denecke K.: Pre-solid varieties. Demonstratio Mathematica, Vol. 27, 3-4 (1994), 741-750. MR 1319418 | Zbl 0841.08006
[8] Evans T.: The lattice of semigroup varieties. Semigroup Forum Vol.2, No 1 (1971) 1-43. MR 0284528 | Zbl 0225.20043
[9] Graczyńska E.: On Normal and Regular Identities and Hyperidentities. Universal and Applied Algebra, Proceedings of the V Universal Algebra Symposium, Turawa, Poland, 3-7 May, 1988, World Scientific, Singapore, New Jersey, London, Hong Kong (1989) 107-135. MR 1084399
[10] Graczyńska E., Schweigert D.: Hyperidentities of a given type. Algebra Universalis 27(1990), 305-318. MR 1058476
[11] Mal’cev I. A.: Iterative Post’s Algebras (russian). Novosibirsk 1976.
[12] Płonka J.: On hyperidentities of some varieties. preprint 1993.
[13] Pöschel R., Reichel M.: Projection algebras and rectangular algebras. General Algebra and Applications, Heldermann-Verlag, Berlin, (1993) 180-194. MR 1209898 | Zbl 0788.08007
[14] Taylor W.: Hyperidentities and hypervarieties. Aequationes Mathematicae 23(1981), 111-127. MR 0667216 | Zbl 0491.08009
[15] Wismath S.: Hyperidentity Bases for rectangular bands and other semigroup varieties. to appear in Journal of the Australian Math. Society. MR 1232760 | Zbl 0816.20053
Search
Partner of
