M-solid generalized non-deterministic varieties
Discussiones Mathematicae General Algebra and Applications (2016)
- Volume: 36, Issue: 1, page 25-43
- ISSN: 1509-9415
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topSomsak Lekkoksung. "M-solid generalized non-deterministic varieties." Discussiones Mathematicae General Algebra and Applications 36.1 (2016): 25-43. <http://eudml.org/doc/286905>.
@article{SomsakLekkoksung2016,
abstract = {A generalized non-deterministic hypersubstitution is a mapping which maps operation symbols of type τ to the set of terms of the same type which does not necessarily preserve the arity. We apply the generalized non-deterministic hypersubstitution to an algebra of type τ and obtain a class of derived algebras of type τ. The generalized non-deterministic hypersubstitutions can be also applied to sets of equations of type τ. We obtain two closure operators which turn out to be a conjugate pair of completely additive closure operators. This allows us to apply the theory of conjugate pairs of additive closure operators to characterize M-solid generalized non-deterministic varieties of algebras.},
author = {Somsak Lekkoksung},
journal = {Discussiones Mathematicae General Algebra and Applications},
keywords = {generalized non-deterministic hypersubstitution; conjugate pair of additive closure operators; M-solid generalized non-deterministic variety},
language = {eng},
number = {1},
pages = {25-43},
title = {M-solid generalized non-deterministic varieties},
url = {http://eudml.org/doc/286905},
volume = {36},
year = {2016},
}
TY - JOUR
AU - Somsak Lekkoksung
TI - M-solid generalized non-deterministic varieties
JO - Discussiones Mathematicae General Algebra and Applications
PY - 2016
VL - 36
IS - 1
SP - 25
EP - 43
AB - A generalized non-deterministic hypersubstitution is a mapping which maps operation symbols of type τ to the set of terms of the same type which does not necessarily preserve the arity. We apply the generalized non-deterministic hypersubstitution to an algebra of type τ and obtain a class of derived algebras of type τ. The generalized non-deterministic hypersubstitutions can be also applied to sets of equations of type τ. We obtain two closure operators which turn out to be a conjugate pair of completely additive closure operators. This allows us to apply the theory of conjugate pairs of additive closure operators to characterize M-solid generalized non-deterministic varieties of algebras.
LA - eng
KW - generalized non-deterministic hypersubstitution; conjugate pair of additive closure operators; M-solid generalized non-deterministic variety
UR - http://eudml.org/doc/286905
ER -
References
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- [3] K. Denecke, P. Glubudom and J. Koppitz, Power clones and Non-detreministic hypersubstitutions, Asian-European J. Math.1 2008, 177-188. doi: 10.1142/S1793557108000175 Zbl1221.08002
- [4] K. Denecke and J. Koppitz, M-solid varieties of algebras (Advances in Mathematics, Vol. 10, Springer, 2006). Zbl1094.08001
- [5] E. Graczyńska and D. Schweigert, Hypervarieties of a given tpye, Algebra Universalis 27 1990, 305-318. Zbl0715.08002
- [6] S. Leeratanavalee and K. Denecke, Generalized Hypersupstitutions and Strongly Solid Varieties, In General Algebra and Applications, Proc. of the '59 th Workshop on General Algebras', '15 th Conference for Young Algebraists Potsdam 2000', Shaker Verlag (2000), 135-145.
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