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In this paper, a visual language, VCP, for queries on complex-value databases is proposed. The main strength of the new language is that it is purely visual: (i) It has no notion of variable, quantification, partiality, join, pattern matching, regular expr ...
Let k be a field of characteristic = 2, and let G be a finite group. The aim of this article is to give a cohomological criterion for the isomorphism of multiples of trace forms of G-Galois algebras over k. The proof uses results concerning multiples ...
One of the most fundamental objects in algebra is the group. There exist plenty of different groups. In the following article we consider some free abelian gorups, cyclic groups, free groups and fundamental groups as well as the products of groups and draw ...
This work contains the study of the algebra called al-Badī‘ fī al-ḥisāb (literally : "the Wonderful on calculation"), written by the Persian mathematician Abu Bakr Muḥammad ibn al-Ḥusain al-Karaǧi (previously known as ...
Our goal is to identify families of relations that are useful for reasoning about software. We describe such families using decidable quantifier-free classes of logical constraints with a rich set of operations. A key challenge is to define such classes of ...
We show that topological Quillen homology of algebras and modules over operads in symmetric spectra can be calculated by realizations of simplicial bar constructions. Working with several model category structures, we give a homotopical proof after showing ...
In homological algebra, to understand commutative rings R, one studies R-modules, chain complexes of R-modules and their monoids, the differential graded R-algebras. The category of R-modules has a rich structure, but too rigid to efficiently work with hom ...
In an application of the notion of twisting structures introduced by Hess and Lack, we define twisted composition products of symmetric sequences of chain complexes that are degreewise projective and finitely generated. Let Q be a cooperad and let BP be th ...
The starting point for this project is the article of Kathryn Hess [11]. In this article, a homotopic version of monadic descent is developed. In the classical setting, one constructs a category D(𝕋) of coalgebras in the Eilenberg-Moore category of ...
We contribute to the classification of finite dimensional algebras under stable equivalence of Morita type. More precisely we give a classification of Erdmann's algebras of dihedral, semi-dihedral and quaternion type and obtain as byproduct the validity of ...
