Commutative bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate additive closure and multiplicative interior operators on this class of algebras.
Which subgroups of the symmetric group Sn arise as invariance groups of n-variable functions defined on a k-element domain? It appears that the higher the difference n-k, the more difficult it is to answer this question. For k ≤ n, the answer is easy: all subgroups of Sn are invariance groups. We give a complete answer in the cases k = n-1 and k = n-2, and we also give a partial answer in the general case: we describe invariance groups when n is much larger than n-k. The proof utilizes Galois connections...
This paper deals with the invariant sets in the group of isometries of a lattice-ordered group. It is shown that all the invariant sets are union of some transitivity subsets of the spheres.
We introduce the inverse topology on the set of all minimal prime ideals of an MV-algebra and show that the set of all minimal prime ideals of , namely , with the inverse topology is a compact space, Hausdorff, -space and -space. Furthermore, we prove that the spectral topology on is a zero-dimensional Hausdorff topology and show that the spectral topology on is finer than the inverse topology on . Finally, by open sets of the inverse topology, we define and study a congruence relation...
In the first section, we introduce the notions of fractional and invertible ideals of semirings and characterize invertible ideals of a semidomain. In section two, we define Prüfer semirings and characterize them in terms of valuation semirings. In this section, we also characterize Prüfer semirings in terms of some identities over its ideals such as for all ideals , of . In the third section, we give a semiring version for the Gilmer-Tsang Theorem, which states that for a suitable family...