Characterization of m-potent Elements in HypG(n) for Some Natural Numbers n
A generalized hypersubstitution of type τ = (n) is a function σ which maps the n-ary operation symbol f to the term σ(f) which does not necessarily preserve the arity. Let HypG(τ ) be the set of all these generalized hypersubstitutions of type (τ ). The set HypG(τ ) with the binary operation “◦G”...
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| Format: | Theses and Dissertations |
| Language: | English |
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เชียงใหม่ : บัณฑิตวิทยาลัย มหาวิทยาลัยเชียงใหม่
2020
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| Online Access: | http://cmuir.cmu.ac.th/jspui/handle/6653943832/69579 |
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| Institution: | Chiang Mai University |
| Language: | English |
| Summary: | A generalized hypersubstitution of type τ = (n) is a function σ which maps the
n-ary operation symbol f to the term σ(f) which does not necessarily preserve the arity.
Let HypG(τ ) be the set of all these generalized hypersubstitutions of type (τ ). The set
HypG(τ ) with the binary operation “◦G” and the identity generalized hypersubstitution
forms a monoid. In studying semigroup theory, the index and the period of an element a
of a finite semigroup are the smallest values of m ≥ 1 and r ≥ 1 such that am+r = am. An
element with the index m and the period 1 is called an m-potent element. In this thesis,
we characterize m-potent elements in this monoid HypG(n) for some natural number n. |
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