Related papers: N-Algebraic Structures and S-N-Algebraic Structure…
For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum algebras and to a new type of Noncommutative…
In previous work, the authors introduced the notion of Q-Koszul algebras, as a tool to "model" module categories for semisimple algebraic groups over fields of large characteristics. Here we suggest the model extends to small…
A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple structures can be presented in block diagonal matrix form (resulting in the Wedderburn decomposition), a general form of polyadic…
We determine the structure of the semisimple group algebra of certain groups over the rationals and over those finite fields where the Wedderburn decompositions have the least number of simple components. We apply our work to obtain similar…
Similar to linear spaces, many examples of quasilinear spaces have a notion of multiplication of the elements. To characterising these examples, in the present paper we generalize the notion of quasilinear spaces and introduce…
In this book, the authors introduce the new notion of superbimatrices and generalize it to supertrimatrices and super n-matrices. Study of these structures is not only interesting and innovative but is also best suited for the computerize…
This book gives a thorough introduction to topological data analysis (TDA), the application of algebraic topology to data science. Algebraic topology is traditionally a very specialized field of math, and most mathematicians have never been…
This work is divided between two main areas: in the theory of multialgebras, we focus mostly on a new definition of what a freely generated object should be in their category, and on how this category is equivalent to another with partially…
Firstly, we introduce a class of new algebraic systems which generalize Hopf quasigroups and Hopf $\pi-$algebras called $Q$-graded Hopf quasigroups, and research some properties of them. Secondly, we define the representations of $Q$-graded…
We adapt the classical framework of algebraic theories to work in the setting of (infinity,1)-categories developed by Joyal and Lurie. This gives a suitable approach for describing highly structured objects from homotopy theory. A central…
We develop a structure theory of connected solvable spherical subgroups in semisimple algebraic groups. Based on this theory, we obtain an explicit classification of all such subgroups up to conjugation.
In this paper we extend of the notion of algebraically closed given in the case of groups and skew fields to an arbitrary h-inductive theory. The main subject of this paper is the study of the notion of positive algebraic closedness and its…
The present survey aims at being a list of Conjectures and Problems in an area of model-theoretic algebra wide open for research, not a list of known results. To keep the text compact, it focuses on structures of finite Morley rank,…
For natural numbers $n$ and $k$, the concepts of $n$-modularly embedded subgroup, $k$-submodular subgroup and $k$-$\mathrm{LM}$-group are given, which generalize, respectively, the concepts of modular subgroup, submodular subgroup and…
In this paper, we introduce the category of blueprints, which is a category of algebraic objects that include both commutative (semi)rings and commutative monoids. This generalization allows a simultaneous treatment of ideals resp.\…
We generalize to arbitrary categories of algebras the notion of an NS-algebra. We do this by using a bimodule property, as we did for defining the general notions of a dendriform and tridendriform algebra. We show that several types of…
The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…
We define algebraic families of (all) morphisms which are purely algebraic analogs of quantum families of (all) maps introduced by P.M. Soltan. Also, algebraic families of (all) isomorphisms are introduced. By using these notions we…
A numerical semigroup is a subset of N containing 0, closed under addition and with finite complement in N. An important example of numerical semigroup is given by the Weierstrass semigroup at one point of a curve. In the theory of…
In this book we use only special types of intervals and introduce the notion of different types of interval linear algebras and interval vector spaces using the intervals of the form [0, a] where the intervals are from Zn or Z+ \cup {0} or…