Residuated lattices form the algebraic counterpart of substructural logics [4]. Rotation construction for t-norms has been introduced in [9] and has been generalized to arbitrary residuated posets in [7]. The reader is referred also to [13, 6, 5]. The rotationannihilation construction has been introduced in [10, 7]. The rotation construction has proved fundamental in the structural description ...

For a system of ordinary differential equations (ODEs) or, more generally, an involutive distribution vector fields, the problem its integration is considered. Among many approaches to this problem, solvable structures provide systematic procedure via Pfaffian that are integrable by quadratures. In paper general than (named cinf-structures) The symmetry condition in concept structure weakened f...

We define the spectral radius and Ptak’s function on a quotient involutive Banach algebra and we extend certains results of V.Ptak to thes quotients. As an application of functional harmonic calculus we obtain theorem similar to those of K.Fan and Von Neumann.

The present paper introduces an approach to construct lexicographic compositions of similarity-based fuzzy orderings. This construction is demonstrated by means of non-trivial examples. As this is a crucial feature of lexicographic composition, the preservation of linearity is studied in detail. We obtain once again that it is essential for meaningful results that the t-norm under consideration...

A 2-form between two sup-lattices L and R is defined to be a suplattice bimorphism L×R → 2. Such 2-forms are equivalent to Galois connections, and we study them and their relation to quantales, involutive quantales and quantale modules. As examples we describe applications to C*-algebras.

We define involutive bases for polynomial ideals and demonstrate their use in calculating direct decompositions of polynomial modules, focusing on the so-called Pommaret bases. The resulting decomposition is the well known Rees decomposition. An overview of other important applications of Pommaret bases is given.