Academic Journal
The α-ideals of co-residuated lattices.
| Τίτλος: | The α-ideals of co-residuated lattices. |
|---|---|
| Συγγραφείς: | Yaning, Zhang1 (AUTHOR), Yao, Wei1 (AUTHOR) yaowei@nuist.edu.cn |
| Πηγή: | Communications in Algebra. 2026, Vol. 54 Issue 9, p3145-3157. 13p. |
| Θεματικοί όροι: | *Ideals (Algebra), *Prime ideals, *Topological spaces, *Residuated lattices, *Nonclassical mathematical logic, *Mathematical logic |
| Περίληψη: | A co-residuated lattice is a logical algebra of non-classical logic systems, built upon the connectives "and not" and "or". Ideals of co-residuated lattices are not only special subalgebraic structures, but also serve as logical deductive systems. This paper focuses on a particular class of ideals, called the α -ideals, which is closely related to annihilators. It is shown that every minimal α -ideal can induce a closure operator on the set of ideals, with the fixed points being precisely the prime α -ideals. Furthermore, the prime α -ideal topological space is defined and its properties related to bases, compact subsets, T 1 , T 2 -separation axioms are investigated. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: | Academic Search Index |
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