On the Cartesian product of the Menger algebras of terms and relational formulas

On the Cartesian product of the Menger algebras of terms and relational formulas

A relational formula which is a first-order formula that only uses relation symbols and terms of arbitrary type is one of the important concepts in the study of algebras and algebraic systems. In this paper, necessary and sufficient conditions for any element in a semigroup whose universe arises fro...

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Date:2025
Main Author: Kumduang, Thodsaporn
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2025
Subjects:
semigroup
term
relational formula
operation
2-potent
20M10
08A05
08A40
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2321
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-2321
record_format ojs
spelling oai:ojs.admjournal.luguniv.edu.ua:article-23212025-10-27T20:24:52Z On the Cartesian product of the Menger algebras of terms and relational formulas Kumduang, Thodsaporn semigroup, term, relational formula, operation, 2-potent 20M10, 08A05, 08A40 A relational formula which is a first-order formula that only uses relation symbols and terms of arbitrary type is one of the important concepts in the study of algebras and algebraic systems. In this paper, necessary and sufficient conditions for any element in a semigroup whose universe arises from the Cartesian product of the Menger algebras of terms and relational formulas to be idempotent and 2-potent are given. By the formula for counting the occurrence of all variables in a formula \(F\), we further show that the order of such pairs is 1, 2, or infinite. Lugansk National Taras Shevchenko University 2025-10-27 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2321 10.12958/adm2321 Algebra and Discrete Mathematics; Vol 40, No 1 (2025) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2321/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2321/1246 Copyright (c) 2025 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2025-10-27T20:24:52Z
collection OJS
language English
topic semigroup
term
relational formula
operation
2-potent
20M10
08A05
08A40
spellingShingle semigroup
term
relational formula
operation
2-potent
20M10
08A05
08A40
Kumduang, Thodsaporn
On the Cartesian product of the Menger algebras of terms and relational formulas
topic_facet semigroup
term
relational formula
operation
2-potent
20M10
08A05
08A40
format Article
author Kumduang, Thodsaporn
author_facet Kumduang, Thodsaporn
author_sort Kumduang, Thodsaporn
title On the Cartesian product of the Menger algebras of terms and relational formulas
title_short On the Cartesian product of the Menger algebras of terms and relational formulas
title_full On the Cartesian product of the Menger algebras of terms and relational formulas
title_fullStr On the Cartesian product of the Menger algebras of terms and relational formulas
title_full_unstemmed On the Cartesian product of the Menger algebras of terms and relational formulas
title_sort on the cartesian product of the menger algebras of terms and relational formulas
description A relational formula which is a first-order formula that only uses relation symbols and terms of arbitrary type is one of the important concepts in the study of algebras and algebraic systems. In this paper, necessary and sufficient conditions for any element in a semigroup whose universe arises from the Cartesian product of the Menger algebras of terms and relational formulas to be idempotent and 2-potent are given. By the formula for counting the occurrence of all variables in a formula \(F\), we further show that the order of such pairs is 1, 2, or infinite.
publisher Lugansk National Taras Shevchenko University
publishDate 2025
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2321
work_keys_str_mv AT kumduangthodsaporn onthecartesianproductofthemengeralgebrasoftermsandrelationalformulas
first_indexed 2025-10-26T02:08:37Z
last_indexed 2025-10-28T02:44:43Z
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