# Presolid varieties of n-semigroups

Avapa Chantasartrassmee; Jörg Koppitz

Discussiones Mathematicae - General Algebra and Applications (2005)

- Volume: 25, Issue: 2, page 221-233
- ISSN: 1509-9415

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topAvapa Chantasartrassmee, and Jörg Koppitz. "Presolid varieties of n-semigroups." Discussiones Mathematicae - General Algebra and Applications 25.2 (2005): 221-233. <http://eudml.org/doc/287688>.

@article{AvapaChantasartrassmee2005,

abstract = {he class of all M-solid varieties of a given type t forms a complete sublattice of the lattice ℒ(τ) of all varieties of algebrasof type t. This gives a tool for a better description of the lattice ℒ(τ) by characterization of complete sublattices. In particular, this was done for varieties of semigroups by L. Polák ([10]) as well as by Denecke and Koppitz ([4], [5]). Denecke and Hounnon characterized M-solid varieties of semirings ([3]) and M-solid varieties of groups were characterized by Koppitz ([9]). In the present paper we will do it for varieties of n-semigroups. An n-semigroup is an algebra of type (n), where the operation satisfies the [i,j]-associative laws for 1 ≤ i ≤ j ≤ n, introduced by Dörtnte ([2]). It is clear that the notion of a 2-semigroup is the same as the notion of a semigroup. Here we will consider the case n ≥ 3.},

author = {Avapa Chantasartrassmee, Jörg Koppitz},

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

keywords = {hypersubstitution; presolid; n-semigroup; -semigroup},

language = {eng},

number = {2},

pages = {221-233},

title = {Presolid varieties of n-semigroups},

url = {http://eudml.org/doc/287688},

volume = {25},

year = {2005},

}

TY - JOUR

AU - Avapa Chantasartrassmee

AU - Jörg Koppitz

TI - Presolid varieties of n-semigroups

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2005

VL - 25

IS - 2

SP - 221

EP - 233

AB - he class of all M-solid varieties of a given type t forms a complete sublattice of the lattice ℒ(τ) of all varieties of algebrasof type t. This gives a tool for a better description of the lattice ℒ(τ) by characterization of complete sublattices. In particular, this was done for varieties of semigroups by L. Polák ([10]) as well as by Denecke and Koppitz ([4], [5]). Denecke and Hounnon characterized M-solid varieties of semirings ([3]) and M-solid varieties of groups were characterized by Koppitz ([9]). In the present paper we will do it for varieties of n-semigroups. An n-semigroup is an algebra of type (n), where the operation satisfies the [i,j]-associative laws for 1 ≤ i ≤ j ≤ n, introduced by Dörtnte ([2]). It is clear that the notion of a 2-semigroup is the same as the notion of a semigroup. Here we will consider the case n ≥ 3.

LA - eng

KW - hypersubstitution; presolid; n-semigroup; -semigroup

UR - http://eudml.org/doc/287688

ER -

## References

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- [2] W. Dörnte, Untersuchungen über einen verallgemeinerten Gruppenbegriff, Math. Z. 29 (1928), 1-19. Zbl54.0152.01
- [3] K. Denecke and Hounnon, All solid varieties of semirings, Journal of Algebra 248 (2002), 107-117.
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- [6] K. Denecke and M. Reichel, Monoids of hypersubstitutions and M-solid varieties, Contributions to General Algebra 9 (1995), 117-126. Zbl0884.08008
- [7] K. Denecke, J. Koppitz and S.L. Wismath, Solid varieties of arbitrary type, Algebra Universalis 48 (2002), 357-378. Zbl1064.08006
- [8] K. Denecke and S.L. Wismath, Hyperidentities and clones, Gordon and Breach Scientific Publisher, 2000.
- [9] J. Koppitz, Hypersubstitutions and groups, Novi Sad J. Math. 34 (2) (2004), 127-139. Zbl1212.20059
- [10] L. Polák, All solid varieties of semigroups, Journal of Algebra 219 (1999), 421-436. Zbl0935.20050
- [11] J. Płonka, Proper and inner hypersubstitutions of varieties, 'Proceedings of the International Conference: 'Summer School on General Algebra and Ordered Sets', Olomouc 1994', Palacký University, Olomouc 1994, 106-115. Zbl0828.08003

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