Superassociative structures of terms and formulas defined by transformations preserving a partition

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Publication Details

Author list: Kumduang, Thodsaporn; Sriwongsa, Songpon;

Publisher: Taylor and Francis Group

Publication year: 2023

ISSN: 0092-7872

eISSN: 1532-4125

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85149314117&doi=10.1080%2f00927872.2023.2180013&partnerID=40&md5=aab43e25d7f1c2b06470f00fe987610e

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, we define terms generated by transformations preserving a partition on a finite set and then construct their superassociative structures. A generating system of such algebra is determined and the freeness in a variety of all superassociative algebras is investigated. The connection between a semigroup of all mappings whose ranges are terms induced by transformations preserving a partition and substitutions is discussed. In views of applications, we apply these mappings to examine identities of a variety in a higher step. Additionally, we generalize our study to algebraic systems and establish a superassociative algebra of a new type of formulas induced by terms defined by transformations preserving a partition. © 2023 Taylor & Francis Group, LLC.

Keywords

Formula, transformation, variety