MATHEMATICA BOHEMICA, Vol. 141, No. 4, pp. 509-517, 2016

$0$-ideals in $0$-distributive posets

Khalid A. Mokbel

Received March 27, 2014.   First published October 13, 2016.

Khalid A. Mokbel, Mathematics Department, Education Faculty, Hodaidah University, P. O. Box 3114, Hodaidah, Yemen, e-mail: khalidalaghbari@yahoo.com

Abstract: The concept of a $0$-ideal in $0$-distributive posets is introduced. Several properties of $0$-ideals in $0$-distributive posets are established. Further, the interrelationships between $0$-ideals and $\alpha$-ideals in $0$-distributive posets are investigated. Moreover, a characterization of prime ideals to be $0$-ideals in $0$-distributive posets is obtained in terms of non-dense ideals. It is shown that every $0$-ideal of a $0$-distributive meet semilattice is semiprime. Several counterexamples are discussed.

Keywords: $0$-distributive poset; $0$-ideal; $\alpha$-ideal; prime ideal; semiprime ideal; dense ideal

Classification (MSC 2010): 06A06, 06A75

DOI: 10.21136/MB.2016.0028-14

Full text available as PDF.

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