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Ordinal sums in the class of L-algebras | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 19 مهر 1405 اصل مقاله (306.33 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2026.33952.1956 | ||
| نویسندگان | ||
| R. A. Borzooei* 1؛ V. Khodadi2؛ M. Aaly Kologani2 | ||
| 1Soft Computing Center, Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran Hatef Higher Education Institute, Zahedan, Iran | ||
| 2Hatef Higher Education Institute, Zahedan, Iran | ||
| چکیده | ||
| This paper initiates a systematic investigation of ordinal sum constructions within the variety of $L$-algebras. We first introduce the concept of an ordinal sum for a family of $L$-algebras and explore its fundamental properties. Our study focuses on the transfer of algebraic properties between the component algebras and their ordinal sum. Specifically, we analyze the behavior of various important classes of $L$-algebras under this construction, including $K$-algebras, $CL$-algebras, and lattices. To deepen the structural analysis, we introduce the notion of an ideal ordinal sum, extending the construction to the level of ideals. We then investigate the ideal theory of ordinal sums, providing a characterization of prime and maximal ideals in terms of the ideals of the constituent algebras. Finally, we explore the global properties of the ordinal sum. We derive necessary and sufficient conditions for the ordinal sum to be sub-directly irreducible, contributing to the understanding of the equational theory of $L$-algebras. Furthermore, we examine the conditions under which the ordinal sum exhibits properties such as semi-simplicity, simplicity, locality, and perfectness. | ||
| کلیدواژه‌ها | ||
| $L$-algebras؛ Ordinal sum؛ Ideal؛ Sub-directly irreducible؛ Semi-simple | ||
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آمار تعداد مشاهده مقاله: 2 تعداد دریافت فایل اصل مقاله: 3 |
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