Pre-solid varieties of semigroups
Denecke, K. ; Koppitz, Jörg
Archivum Mathematicum, Tome 031 (1995), p. 171-181 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 1995-01-01
Classification:  08B15,  20M07
@article{107538,
     author = {K. Denecke and J\"org Koppitz},
     title = {Pre-solid varieties of semigroups},
     journal = {Archivum Mathematicum},
     volume = {031},
     year = {1995},
     pages = {171-181},
     zbl = {0842.20049},
     mrnumber = {1368256},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107538}
}
Denecke, K.; Koppitz, Jörg. Pre-solid varieties of semigroups. Archivum Mathematicum, Tome 031 (1995) pp. 171-181. http://gdmltest.u-ga.fr/item/107538/

Denecke K.; Koppitz J. Hyperassociative semigroups, Semigroup Forum, Vol. 49,(1994) 41-48. (1994) | MR 1272861

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. (1991) | MR 1143072 | Zbl 0759.08005

Denecke K.; Wismath S. L. Solid varieties of semigroups, Semigroup Forum, Vol. 48, (1994) 219-234. (1994) | MR 1256690 | Zbl 0797.20045

Denecke K.; Płonka J. On regularizations and normalizations of solid varieties, in: General Algebra and Discrete Mathematics, Berlin 1995, 83-92. (1995)

Denecke K.; Koppitz J. Presolid varieties of commutative semigroups, preprint 1993. (1993) | MR 1384792

Denecke K.; Lau D.; Pöschel R.; Schweigert D. Free Clones and Solid Varieties, preprint 1993. (1993) | MR 1336152

Denecke K. Pre-solid varieties, Demonstratio Mathematica, Vol. 27, 3-4 (1994), 741-750. (1994) | MR 1319418 | Zbl 0841.08006

Evans T. The lattice of semigroup varieties, Semigroup Forum Vol.2, No 1 (1971) 1-43. (1971) | MR 0284528 | Zbl 0225.20043

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. (1988) | MR 1084399

Graczyńska E.; Schweigert D. Hyperidentities of a given type, Algebra Universalis 27(1990), 305-318. (1990) | MR 1058476

Mal’Cev I. A. Iterative Post’s Algebras (russian), Novosibirsk 1976. (1976)

Płonka J. On hyperidentities of some varieties, preprint 1993. (1993)

Pöschel R.; Reichel M. Projection algebras and rectangular algebras, General Algebra and Applications, Heldermann-Verlag, Berlin, (1993) 180-194. (1993) | MR 1209898 | Zbl 0788.08007

Taylor W. Hyperidentities and hypervarieties, Aequationes Mathematicae 23(1981), 111-127. (1981) | MR 0667216 | Zbl 0491.08009

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