# Pre-strongly solid varieties of commutative semigroups

Sarawut Phuapong; Sorasak Leeratanavalee

Discussiones Mathematicae - General Algebra and Applications (2011)

- Volume: 31, Issue: 1, page 27-45
- ISSN: 1509-9415

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topSarawut Phuapong, and Sorasak Leeratanavalee. "Pre-strongly solid varieties of commutative semigroups." Discussiones Mathematicae - General Algebra and Applications 31.1 (2011): 27-45. <http://eudml.org/doc/276629>.

@article{SarawutPhuapong2011,

abstract = {Generalized hypersubstitutions are mappings from the set of all fundamental operations into the set of all terms of the same language do not necessarily preserve the arities. Strong hyperidentities are identities which are closed under the generalized hypersubstitutions and a strongly solid variety is a variety which every its identity is a strong hyperidentity. In this paper we give an example of pre-strongly solid varieties of commutative semigroups and determine the least and the greatest pre-strongly solid variety of commutative semigroups.},

author = {Sarawut Phuapong, Sorasak Leeratanavalee},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {generalized hypersubstitution; pre-strongly solid variety; commutative semigroup; generalized hypersubstitutions; pre-strongly solid varieties of semigroups; strong hyperidentities; varieties of commutative semigroups},

language = {eng},

number = {1},

pages = {27-45},

title = {Pre-strongly solid varieties of commutative semigroups},

url = {http://eudml.org/doc/276629},

volume = {31},

year = {2011},

}

TY - JOUR

AU - Sarawut Phuapong

AU - Sorasak Leeratanavalee

TI - Pre-strongly solid varieties of commutative semigroups

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2011

VL - 31

IS - 1

SP - 27

EP - 45

AB - Generalized hypersubstitutions are mappings from the set of all fundamental operations into the set of all terms of the same language do not necessarily preserve the arities. Strong hyperidentities are identities which are closed under the generalized hypersubstitutions and a strongly solid variety is a variety which every its identity is a strong hyperidentity. In this paper we give an example of pre-strongly solid varieties of commutative semigroups and determine the least and the greatest pre-strongly solid variety of commutative semigroups.

LA - eng

KW - generalized hypersubstitution; pre-strongly solid variety; commutative semigroup; generalized hypersubstitutions; pre-strongly solid varieties of semigroups; strong hyperidentities; varieties of commutative semigroups

UR - http://eudml.org/doc/276629

ER -

## References

top- [1] K. Denecke, D. Lau, R. Pöschel and D. Schweigert, Hypersubstitutions, Hyperequational Classes and Clones Congruence, Contributions to General Algebras 7 (1991), 97-118. Zbl0759.08005
- [2] K. Denecke and S.L. Wismath, Hyperidentities and Clones, Gordon and Breach Scientific Publishers 2000. Zbl0960.08001
- [3] E. Graczyńska and D. Schweigert, Hyperidentities of a given type, Algebra Universalis 27 (1990), 305-18. doi: 10.1007/BF01190711 Zbl0715.08002
- [4] S. Leeratanavalee and K. Denecke, Generalized Hypersubstitutions and Strongly Solid Varieties, p. 135-145 in: General Algebra and Applications, 'Proc. of the 59 th Workshop on General Algebra', '15 th Conference for Young Algebraists Potsdam 2000', Shaker Verlag 2000.
- [5] S. Leeratanavalee and S. Phatchat, Pre-Strongly Solid and Left-Edge(Right-Edge)-Strongly Solid Varieties of Semigroups, International Journal of Algebra 1 (5) (2007), 205-226. Zbl1127.08003
- [6] J. Płonka, Proper and Inner Hypersubstitutions of Varieties, p. 106-155 in: General Algebra and Ordered Sets, 'Proc. of the International Conference: Summer School on General Algebra and Ordered Sets 1994', Palacky University Olomouc 1994.

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