Pre-solid varieties of semigroups

K. Denecke; Jörg Koppitz

Archivum Mathematicum (1995)

  • Volume: 031, Issue: 3, page 171-181
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Denecke, K., and Koppitz, Jörg. "Pre-solid varieties of semigroups." Archivum Mathematicum 031.3 (1995): 171-181. <http://eudml.org/doc/247689>.

@article{Denecke1995,
abstract = {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.},
author = {Denecke, K., Koppitz, Jörg},
journal = {Archivum Mathematicum},
keywords = {hyperidentity; pre-hyperidentity; pre-solid variety; pre-hyperidentity; pre-solid varieties; solid varieties; solid semigroup variety; varieties of semigroups; rectangular bands; medial semigroup varieties},
language = {eng},
number = {3},
pages = {171-181},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Pre-solid varieties of semigroups},
url = {http://eudml.org/doc/247689},
volume = {031},
year = {1995},
}

TY - JOUR
AU - Denecke, K.
AU - Koppitz, Jörg
TI - Pre-solid varieties of semigroups
JO - Archivum Mathematicum
PY - 1995
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 031
IS - 3
SP - 171
EP - 181
AB - 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.
LA - eng
KW - hyperidentity; pre-hyperidentity; pre-solid variety; pre-hyperidentity; pre-solid varieties; solid varieties; solid semigroup variety; varieties of semigroups; rectangular bands; medial semigroup varieties
UR - http://eudml.org/doc/247689
ER -

References

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  1. Denecke K., Koppitz J., Hyperassociative semigroups, Semigroup Forum, Vol. 49,(1994) 41-48. (1994) MR1272861
  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. (1991) Zbl0759.08005MR1143072
  3. Denecke K., Wismath S. L., Solid varieties of semigroups, Semigroup Forum, Vol. 48, (1994) 219-234. (1994) Zbl0797.20045MR1256690
  4. Denecke K., Płonka J., On regularizations and normalizations of solid varieties, in: General Algebra and Discrete Mathematics, Berlin 1995, 83-92. (1995) 
  5. Denecke K., Koppitz J., Presolid varieties of commutative semigroups, preprint 1993. (1993) MR1384792
  6. Denecke K., Lau D., Pöschel R., Schweigert D., Free Clones and Solid Varieties, preprint 1993. (1993) MR1336152
  7. Denecke K., Pre-solid varieties, Demonstratio Mathematica, Vol. 27, 3-4 (1994), 741-750. (1994) Zbl0841.08006MR1319418
  8. Evans T., The lattice of semigroup varieties, Semigroup Forum Vol.2, No 1 (1971) 1-43. (1971) Zbl0225.20043MR0284528
  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. (1988) MR1084399
  10. Graczyńska E., Schweigert D., Hyperidentities of a given type, Algebra Universalis 27(1990), 305-318. (1990) MR1058476
  11. Mal’cev I. A., Iterative Post’s Algebras (russian), Novosibirsk 1976. (1976) 
  12. Płonka J., On hyperidentities of some varieties, preprint 1993. (1993) 
  13. Pöschel R., Reichel M., Projection algebras and rectangular algebras, General Algebra and Applications, Heldermann-Verlag, Berlin, (1993) 180-194. (1993) Zbl0788.08007MR1209898
  14. Taylor W., Hyperidentities and hypervarieties, Aequationes Mathematicae 23(1981), 111-127. (1981) Zbl0491.08009MR0667216
  15. Wismath S., Hyperidentity Bases for rectangular bands and other semigroup varieties, to appear in Journal of the Australian Math. Society. Zbl0816.20053MR1232760

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