Khalid A. Mokbel, Mathematics Department, Education Faculty, Hodaidah University, P. O. Box 3114, Al Hudaydah, Yemen, e-mail: khalidalaghbari@yahoo.com
Abstract: The concept of $\alpha$-ideals in posets is introduced. Several properties of $\alpha$-ideals in $0$-distributive posets are studied. Characterization of prime ideals to be $\alpha$-ideals in $0$-distributive posets is obtained in terms of minimality of ideals. Further, it is proved that if a prime ideal $I$ of a $0$-distributive poset is non-dense, then $I$ is an $\alpha$-ideal. Moreover, it is shown that the set of all $\alpha$-ideals $\alpha\mathop Id(P)$ of a poset $P$ with $0$ forms a complete lattice. A result analogous to separation theorem for finite $0$-distributive posets is obtained with respect to prime $\alpha$-ideals. Some counterexamples are also given.
Keywords: $0$-distributive poset; ideal; $\alpha$-ideal; prime ideal; non-dense ideal; minimal ideal; annihilator ideal
Classification (MSC 2010): 06A06, 06A75
Full text available as PDF.
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
