The problem of characterization of the structure of MTL-algebras, which form an equivalent algebraic semantics for Monoidal T-norm Based Logic (see [9]) in the sense of Blok and Pigozzi (see [3]), is still far from being solved. Since MTL-algebras are in fact subdirect products of chains, it suffices to investigate only the structure of MTL-chains if we want to characterize the structure of MTL...

Recently, Vemuri and Jayaram proposed a novel method of generating fuzzy implications, called the ~-composition, from a given pair of fuzzy implications (Vemuri and Jayaram, 2014). However, as with any generation process, the ~-composition does not always generate new fuzzy implications. In this work, we study the generative power of the ~-composition. Towards this end, we study some specific f...

In 2001, S. Bulman-Fleming et al. initiated the study of three flatness properties (weakly kernel flat, principally weakly kernel flat, translation kernel flat) of right acts $A_{S}$ over a monoid $S$ that can be described by means of when the functor $A_{S} otimes -$ preserves pullbacks. In this paper, we extend these results to $S$-posets and present equivalent descriptions of weakly kernel p...

‎ In the present article‎, ‎we study some categorical properties of the category {$bf‎ Cpo_{Sep}$-$S$} of all {separately strict $S$-cpo's}; cpo's equipped with‎ a compatible right action of a separately strict cpo-monoid $S$ which is‎ strict continuous in each component‎. ‎In particular‎, we show that this category is reflective and coreflective in the‎ category of $S$-cpo's‎, ‎find the free a...

We describe a re ned superposition calculus for cancellative abelian monoids. They encompass not only abelian groups, but also such ubiquitous structures as the natural numbers or multisets. Both the AC axioms and the cancellation law are di cult for a general purpose superposition theorem prover, as they create many variants of clauses which contain sums. Our calculus requires neither explicit...

A cancellative hypergraph has no three edges A;B;C with ADBCC: We give a new short proof of an old result of Bollobás, which states that the maximum size of a cancellative triple system is achieved by the balanced complete tripartite 3-graph. One of the two forbidden subhypergraphs in a cancellative 3-graph is F5 1⁄4 fabc; abd; cdeg: For nX33 we show that the maximum number of triples on n vert...

in 2001, s. bulman-fleming et al. initiated the study of three flatness properties (weakly kernel flat, principally weakly kernel flat, translation kernel flat) of right acts $a_{s}$ over a monoid $s$ that can be described by means of when the functor $a_{s} otimes -$ preserves pullbacks. in this paper, we extend these results to$s$-posets and present equivalent descriptions of weakly kernel po...

Let H be a commutative semigroup with unit element such that every non-unit can be written as a finite product of irreducible elements (atoms). For every k ∈ N, let Uk(H) denote the set of all ` ∈ N with the property that there are atoms u1, . . . , uk, v1, . . . , v` such that u1 · . . . · uk = v1 · . . . · v` (thus, Uk(H) is the union of all sets of lengths containing k). The Structure Theore...

The class of finitely presented algebras A over a field K with a set of generators x1, . . . , xn and defined by homogeneous relations of the form xi1xi2 · · · xil = xσ(i1)xσ(i2) · · · xσ(il), where l ≥ 2 is a given integer and σ runs through a subgroup H of Symn, is considered. It is shown that the underlying monoid Sn,l(H) = 〈x1, x2, . . . , xn | xi1xi2 · · · xil = xσ(i1)xσ(i2) · · · xσ(il), ...