Free involutive Hom-semigroups and Hom-associative algebras
Li Guo, Shanghua Zheng
TL;DR
This paper constructs free Hom-semigroups with an involutive, multiplicative unary operation using bracketed words, leading to free Hom-associative algebras under similar conditions.
Contribution
It introduces a new construction method for free Hom-semigroups and Hom-associative algebras with involutive, multiplicative unary operations.
Findings
Constructed free Hom-semigroups via bracketed words.
Derived free Hom-associative algebras from the semigroup construction.
Established properties of these free algebraic structures.
Abstract
In this paper we construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence, we obtain free Hom-associative algebras generated by a set under the same conditions for the unary operation.
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