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Extension of stabilizers on subtraction algebras | ||
| Journal of Mahani Mathematical Research | ||
| دوره 13، شماره 4 - شماره پیاپی 29، اسفند 2024، صفحه 165-179 اصل مقاله (458.35 K) | ||
| نوع مقاله: Special Issue Dedicated to Prof. Esfandiar Eslami | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2024.23142.1599 | ||
| نویسندگان | ||
| Saeide Zahiri* 1؛ Farshad Nahangi2 | ||
| 1Department of Mathematics, Faculty of Science, Higher Education Center of Eghlid, Eghlid, Iran | ||
| 2ASU School of Computing and Augmented Intelligence, Tempe, AZ, USA | ||
| چکیده | ||
| This paper explores the intersection between the class of bounded subtraction algebras and the class of Boolean algebras, demonstrating their equivalence. It introduces the concepts of stabilizers for subsets and the stabilizers of one subset with respect to another within subtraction algebras. The study reveals that both the stabilizer of a subset and the stabilizer of an ideal with respect to another ideal are, in fact, ideals themselves. Investigating the impact of stabilizers on product and quotient subtraction algebras is a focal point. Additionally, a novel concept termed the ”stabilizer operation” is defined, and it is proven that the collection of ideals endowed with a binary stabilizer operator forms a bounded Hilbert algebra. | ||
| کلیدواژه‌ها | ||
| (Bounded) Subtraction algebra؛ Stabilizer؛ Hilbert algebra | ||
| مراجع | ||
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[15] Zelinka, B. (1995). Subtraction Semigroups. Mathematica Bohemica, 120, 445-447. | ||
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