SOME PROPERTIES ON DERIVATIONS OF LATTICES | ||
| Journal of Algebraic Systems | ||
| دوره 9، شماره 1، آذر 2021، صفحه 21-33 اصل مقاله (145.83 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2020.7088.1347 | ||
| نویسندگان | ||
| Mayuka F Kawaguchi1؛ Michiro KONDO* 2 | ||
| 1Graduate School of Information Science and Technology, Hokkaido University, P.O.Box 060-0814 Sapporo, Japan | ||
| 2Department of Mathematics, School of System Design and Technology, Tokyo Denki University, P.O.Box 120-8551 Tokyo, Japan | ||
| چکیده | ||
| In this paper we consider some properties of derivations of lattices and show that (i) for a derivation $d$ of a lattice $L$ with the maximum element $1$, it is monotone if and only if $d(x) \le d(1)$ for all $x\in L$ (ii) a monotone derivation $d$ is characterized by $d(x) = x\wedge d(1)$ and (iii) simple characterization theorems of modular lattices and of distributive lattices are given by derivations. We also show that, for a distributive lattice $L$ and a monotone derivation $d$ of it, the set ${\rm Fix}_d(L)$ of all fixed points of $d$ is isomorphic to the lattice $L/\ker (d)$. We provide a counter example to the result (Theorem 4) proved in [3]. | ||
| کلیدواژهها | ||
| derivation؛ order-preserving؛ modular lattice؛ distributive lattice | ||
| مراجع | ||
|
1. N. O. Alshehri, Generalized derivations of lattices, Int. J. Contemp. Math. Sciences, 5 (2010), 629–640.
2. M. Aşci and Ş. Ceray, Generalized (f; g)-derivations of lattices, Math. Sciencesand Applications E-note, 1(2) (2013), 56–62. 3. Y. Çeven and M. A. Öztürk, On f-derivations of lattices, Bull. Korean Math. Soc., 45 (2008), 701–707. 4. L. Ferrari, On derivations of lattices, Pure Mathematics and Applications, 12 (2001), 365–382. 5. E. Posner, Derivations in prime rings, Proc. Am. Math. Soc., 8 (1957), 1093–1100. 6. G. Szász, Derivations of lattices, Acta Sci. Math. (Szeged), 37 (1975), 149–154. 7. X. L. Xin, T. Y. Li and J. H. Lu, On derivations of lattices, Information Sciences 178 (2008), 307–316. | ||
|
آمار تعداد مشاهده مقاله: 581 تعداد دریافت فایل اصل مقاله: 720 |
||