Let k be a commutative ring, A a commutative k-algebra and D the filtered ring of k-linear differential operators of A. We prove that: (1) The graded ring grD admits a canonical embedding θ into the graded dual of the symmetric algebra of the module ΩA/k of differentials of A over k, which has a canonical divided power structure. (2) There is a canonical morphism θ from the divided power algebr...

the notion of vague ideals in pseudo mv-algebras is introduced,and several properties are investigated. conditions for a vague set to be avague ideal are provided. conditions for a vague ideal to be implicative aregiven. characterizations of (implicative, prime) vague ideals are discussed.the smallest vague ideal containing a given vague set is established. primeand implicative extension proper...

Spider diagrams provide a visual logic to express relations between sets and their elements, extending the expressiveness of Venn diagrams. Sound and complete inference systems for spider diagrams have been developed and it is known that they are equivalent in expressive power to monadic first-order logic with equality, MFOL[1⁄4]. languages that are finite unions of languages of the form K G , ...

We study D0L power series over commutative semirings. We show that a sequence (cn)n 0 of nonzero elements of a eld A is the coe cient sequence of a D0L power series if and only if there exist a positive integer k and integers i for 1 i k such that cn+k = c 1 n+k 1c 2 n+k 2 : : : c k n for all n 0. As a consequence we solve the equivalence problem of D0L power series over computable elds. TUCS R...

Given a commutative Noetherian local ring R, the linearity defect of a finitely generated R-module M , denoted ldR(M), is an invariant that measures how far M and its syzygies are from having a linear resolution. Motivated by a positive known answer in the graded case, we study the question of whether ldR(k) < ∞ implies ldR(k) = 0. We give answers in special cases, and we discuss several interp...

‎in this paper‎, ‎the notion of the radical of a filter in‎ ‎residuated lattices is defined and several characterizations of‎ ‎the radical of a filter are given‎. ‎we show that if f is a‎ ‎positive implicative filter (or obstinate filter)‎, ‎then‎ ‎rad(f)=f‎. ‎we proved the extension theorem for radical of filters in residuated lattices‎. ‎also‎, ‎we study the radical‎ ‎of filters in linearly o...

The generalized state space of a commutative C-algebra, denoted SH(C(X)), is the set of positive unital maps from C(X) to the algebra B(H) of bounded linear operators on a Hilbert space H. C-convexity is one of several non-commutative analogs of convexity which have been discussed in this context. In this paper we show that a C-extreme point of SH(C(X)) satisfies a certain spectral condition on...

This paper is devoted to the foldness theory of implicative ideals in BCK-algebras. We use the fuzzy point concept to give some characterizations of fuzzy n-fold implicative ideals and establish some relationships with various n-fold ideals. We also construct some algorithms for studying the foldness of implicative ideals in BCK-algebras. AMS Mathematics Subject Classification: 06F35, 13A15, 8A...

The commutative ambiguity cambG,X of a context-free grammar G with start symbol X assigns to each Parikh vector v the number of distinct leftmost derivations yielding a word with Parikh vector v. Based on the results on the generalization of Newton’s method to ω-continuous semirings [EKL07b, EKL07a, EKL10], we show how to approximate cambG,X by means of rational formal power series, and give a ...

We study the commutative positive varieties of languages closed under various operations: shuffle, renaming and product over one-letter alphabets. Most monoids considered in this paper are finite. In particular, we use the term variety of monoids for variety of finite monoids. Similarly, all languages considered in this paper are regular languages and hence their syntactic monoid is finite.