On (semi)topology L-algebras | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 5، دوره 18، شماره 1، اردیبهشت 2023، صفحه 81-103 اصل مقاله (567.03 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.52547/cgasa.2023.103121 | ||
| نویسنده | ||
| Mona Aaly Kologani | ||
| Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran | ||
| چکیده | ||
| Here, we define (semi)topological L-algebras and some related results are approved. Then we deduce conditions that mention an L-algebra to be a semi-topological or a topological L-algebra and we check some attributes of them. Chiefly, we display in an L-algebra L, if (L, ↠, τ ) is a semi-topological L-algebra and {1} is an open set or L is bounded and satisfies the double negation property, then (L,τ) is a topological L-algebra. Finally, we construct a discrete topology on a quotient L-algebra, under suit- able conditions. Also, different kinds of topology such as T0 and Hausdorff are investigated. | ||
| کلیدواژهها | ||
| L-algebra؛ ideal؛ (semi)topological L-algebra؛ quotient L-algebra؛ Hausdorff | ||
| مراجع | ||
|
[1] Aaly Kologani, M., Kouhestani, N., and Borzooei, R.A., On topological semi-hoops, Quasigroup Related Systems 25 (2017), 165-179.
[2] Borzooei, R.A., Rezaei, G.R., and Kouhestani, N., On (semi)topologica BL-algebras, Iran. J. Math. Sci. Info. 6(1) (2011), 59-77.
[3] Borzooei, R.A., Rezaei, G.R., and Kouhestani, N., Metrizability on (semi)topological BL-algebras, Soft Comput. 16(10) (2012), 1681-1690.
[4] Borzooei, R.A., Rezaei, G.R., and Kouhestani, N., Separation axioms in (semi)topological quotient BL-algebras, Soft Comput. 16(7) (2012), 1219-1227.
[5] Borzooei, R.A., Kouhestani, N., and Aaly Kologani, M., On (semi)topological hoop algebras, Quasigroup Related Systems 27 (2019), 161-174.
[6] Bosbach, B., Concerning cone algebras, Algebra Univers. 15 (1982), 58-66.
[7] Drinfeld, V.G., “On some unsolved problems in quantum group theory”, in: P.P. Kulish (Ed.), Quantum Groups (Leningrad, 1990), Lecture Notes in Mathematics, Vol. 1510, Springer, Berlin, 1992.
[8] Etingof, P., Geometric crystals and set-theoretical solutions to the quantum Yang- Baxter equation, Comm. Algebra. 31(4) (2003), 1961-1973.
[9] Etingof, P. and Gelaki, S., A method of construction of finite-dimensional triangular semisimple Hopf algebras, Math. Res. Lett. 5 (1998), 551-561.
[10] Etingof, P., Schedler, T., and Soloviev, A., Set-theoretical solutions to the quantum Yang-Baxter equation, Duke Math. J. 100 (1999), 169-209.
[11] Gateva-Ivanova, T., Noetherian properties of skew-polynomial rings with binomial relations, Trans. Amer. Math. Soc. 343 (1994), 203-219.
[12] Gateva-Ivanova, T., Skew polynomial rings with binomial relations, J. Algebra 185 (1996), 710-753.
[13] Gateva-Ivanova,T.,VandenBergh,M.,SemigroupsofI-type,J.Algebra206(1998), 97-112.
[14] Husain, T., “Introduction to Topological Groups”, Philadelphia: WB Sunders Com- pany, 1966.
[15] Munkres, J.R., “Topology a First Course”, Englewood Cliffs, New Jersey: Prentice- Hall 23, 1975.
[16] Rump,W.,Adecompositiontheoremforsquare-freeunitarysolutionsofthequantum Yang-Baxter equation, Adv. Math. 193, (2005), 40–55.
[17] Rump, W., L-algebras, self-similarity, and l-groups, J. Algebra 320 (2008), 2328- 2348.
[18] Rump, W., Semidirect products in algebraic logic and solutions of the quantum Yang- Baxter equation, J. Algebra its Appl. 7 (2008), 471-490.
[19] Rump, W. and Yang, Y., Interval in l-groups as L-algebras, Algebra Univers. 67(2) (2012), 121-130.
[20] Tate, J. and Van den Bergh, M., Homological properties of Sklyanin algebras, Invent. Math. 124 (1996), 619-647.
[21] Traczyk, T., On the structure of BCK-algebras with zxyx = zyxy, Japanese J. Math. 33 (1988), 319-324.
[22] Veselov, A.P., Yang-Baxter maps and integrable dynamics, Phys. Lett. A 314(3), (2002), DOI:10.1016/S0375-9601(03)00915-0.
[23] Wu, Y.L., Wang, J., and Yang, Y.C., Lattice-ordered effect algebras and L-algebras, Fuzzy Sets and Systems 369 (2019), 103-113.
[24] Wu, Y.L. and Yang, Y.C., Orthomodular lattices as L-algebras, Soft Comput. 24 (2020), 14391-14400. | ||
|
آمار تعداد مشاهده مقاله: 265 تعداد دریافت فایل اصل مقاله: 876 |
||