an:06502699
Zbl 1351.06003
Kavishwar, Shubhangi; Joshi, Vinayak
A note on prime ideal principle in lattices
EN
Asian-Eur. J. Math. 8, No. 2, Article ID 1550024, 12 p. (2015).
00346287
2015
j
06B10 06D75
distributive lattice; \(0\)-distributive lattice; prime ideal; ``maximum implies prime'' principle
Authors' abstract: In this paper, we introduce a prime ideal principle (PIP) in lattices and use it to prove that certain ideals in lattices are prime ideals. Moreover, our results yield a unification of known results of \textit{M. H. Stone} [Trans. Am. Math. Soc. 40, 37--111 (1936; Zbl 0014.34002; JFM 62.0033.04)], \textit{V. A. Gorbunov} and \textit{V. I. Tumanov} [Algebra Univers. 16, 250--252 (1983; Zbl 0516.06006)], \textit{Y. Rav} [J. Pure Appl. Algebra 56, No. 2, 105--118 (1989; Zbl 0665.06006)] etc. on prime ideals.
Marcel Wild (Stellenbosch)
Zbl 0014.34002; JFM 62.0033.04; Zbl 0516.06006; Zbl 0665.06006