×

zbMATH — the first resource for mathematics

A note on prime ideal principle in lattices. (English) Zbl 1351.06003
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 M. H. Stone [Trans. Am. Math. Soc. 40, 37–111 (1936; Zbl 0014.34002; JFM 62.0033.04)], V. A. Gorbunov and V. I. Tumanov [Algebra Univers. 16, 250–252 (1983; Zbl 0516.06006)], Y. Rav [J. Pure Appl. Algebra 56, No. 2, 105–118 (1989; Zbl 0665.06006)] etc. on prime ideals.

MSC:
06B10 Lattice ideals, congruence relations
06D75 Other generalizations of distributive lattices
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Anderson D. D., Acta Sci. Math. (Szeged) 59 pp 61– (1994)
[2] DOI: 10.1215/S0012-7094-50-01704-2 · Zbl 0041.36408 · doi:10.1215/S0012-7094-50-01704-2
[3] DOI: 10.1023/A:1008611926427 · Zbl 0980.08001 · doi:10.1023/A:1008611926427
[4] DOI: 10.1007/BF01191774 · Zbl 0516.06006 · doi:10.1007/BF01191774
[5] Grätzer G., General Lattice Theory (1998)
[6] Grätzer G., Acta. Sci. Math. (Szeged) 19 pp 82– (1958)
[7] DOI: 10.1007/BF02066675 · Zbl 0115.01901 · doi:10.1007/BF02066675
[8] Jayaram C., Indian J. Pure Appl. Math. 17 pp 331– (1986)
[9] DOI: 10.2478/s11533-013-0206-z · Zbl 1288.06002 · doi:10.2478/s11533-013-0206-z
[10] Joshi V., Math. Bohem. 130 pp 73– (2005)
[11] Kaplansky I., Commutative Rings (1974)
[12] DOI: 10.3792/pja/1195522165 · Zbl 0144.25401 · doi:10.3792/pja/1195522165
[13] DOI: 10.1016/j.jalgebra.2007.07.016 · Zbl 1168.13002 · doi:10.1016/j.jalgebra.2007.07.016
[14] Pawar Y. S., Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 49 pp 63– (2010)
[15] Pawar Y. S., Indian J. Pure Appl. Math. 24 pp 435– (1993)
[16] DOI: 10.4153/CMB-1978-080-6 · Zbl 0413.06002 · doi:10.4153/CMB-1978-080-6
[17] DOI: 10.1016/0022-4049(89)90140-0 · Zbl 0665.06006 · doi:10.1016/0022-4049(89)90140-0
[18] DOI: 10.1017/S1446788700010715 · Zbl 0242.13003 · doi:10.1017/S1446788700010715
[19] Stone M. H., Trans. Amer. Math. Soc. 40 pp 37– (1936)
[20] Thakare N. K., J. Indian Math. Soc. 71 pp 13– (2004)
[21] Varlet J., Bull. Soc. Roy. Sci. Liége 37 pp 149– (1968)
[22] DOI: 10.1007/s11083-004-2862-x · doi:10.1007/s11083-004-2862-x
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.