All Regular Elements in Hyp_G(2)
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In this paper we consider mappings which map the binary operation symbol f to the term σ(f) which do not necessarily preserve the arities. We call these mappings generalized hypersubstitutions. Any generalized hypersubstitution σ can be extended to a mapping σ on the set of all terms of type τ ＝ (2). We define a binary operation on the set Hyp_G(2) of all generalized hypersubstitutions of type τ ＝ (2) by using this extension. The set Hyp_G(2) together with the identity generalized hypersubstitution σ_(id) which maps f to the term f(x₁, x₂) forms a monoid. We determine all regular elements of this monoid.
Abstract
In this paper we consider mappings which map the binary operation symbol f to the term σ(f) which do not necessarily preserve the arities. We call these mappings generalized hypersubstitutions. Any generalized hypersubstitution σ can be extended to a mapping σ on the set of all terms of type τ ＝ (2). We define a binary operation on the set Hyp_G(2) of all generalized hypersubstitutions of type τ ＝ (2) by using this extension. The set Hyp_G(2) together with the identity generalized hypersubstitution σ_(id) which maps f to the term f(x₁, x₂) forms a monoid. We determine all regular elements of this monoid.
참고문헌 (5)
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- Koppitz, J., "M-Solid Varieties of Algebras" (2006), Springer Science+Business Media, Inc
- Sorasak Leeratanavalee, "Structural Properties of Generalized Hypersubstitutions", Kyungpook Mathematical Journal, 44(2), pp.261~267 (2004), 경북대학교 자연과학대학 수학과
- Leeratanavalee, S., "Generalized Hypersubstitutions and Strongly Solid Varieties", In General Algebra and Applications, Proc. of the \59 th Workshop on General Algebra", \15 th Conference for Young Algebraists Potsdam 2000", pp.135~145 (2000), Shaker Verlag