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Ultra LI-ideals in lattice implication algebras and MTL-algebra | | Xiaohong Zhang
; Keyun Qin
; Wieslaw A. Dudek
; | | Date: |
21 Oct 2007 | | Abstract: | A mistake concerning the ultra extit{LI}-ideal of a lattice implication
algebra is pointed out, and some new sufficient and necessary conditions for an
extit{LI}-ideal to be an ultra extit{LI}-ideal are given. Moreover, the
notion of an extit{LI}-ideal is extended to MTL-algebras, the notions of a
(prime, ultra, obstinate, Boolean) extit{LI}-ideal and an extit{ILI}-ideal
of an MTL-algebra are introduced, some important examples are given, and the
following notions are proved to be equivalent in MTL-algebra: (1) prime proper
extit{LI}-ideal and Boolean extit{LI}-ideal, (2) prime proper
extit{LI}-ideal and extit{ILI}-ideal, (3) proper obstinate
extit{LI}-ideal, (4) ultra extit{LI}-ideal. | | Source: | arXiv, 0710.3887 | | Services: | Forum | Review | PDF | Favorites | |
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