Related papers: Biring of Matrices
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
We give an explicit formula for the Hilbert Series of an algebra defined by a linearly presented, standard graded, residual intersection of a grade three Gorenstein ideal.
We interpret several constructions with C*-algebras as colimits in the bicategory of correspondences. This includes crossed products for actions of groups and crossed modules, Cuntz-Pimsner algebras of proper product systems, direct sums…
In this paper, we develop 2-dimensional algebraic theory which closely follows the classical theory of modules. The main results are giving definitions of 2-module and the representation of 2-ring. Moreover, for a 2-ring $\cR$, we prove…
Conference matrices are used to define complex structures on real vector spaces. Certain lattices in these spaces become modules for rings of quadratic integers. Multiplication of these lattices by non-principal ideals yields simple…
We describe Artin's braid group on a (fixed) finite number of strings as a crossed module over itself. In particular, we interpret the braid relations as crossed module structure relations.
The study of a certain class of matrix integrals can be motivated by their interpretation as counting objects of knot theory such as alternating prime links, tangles or knots. The simplest such model is studied in detail and allows to…
Any associative bilinear multiplication on the set of n-by-n matrices over some field of characteristic not two, that makes the same vectors orthogonal and has the same trace as ordinary matrix multiplication, must be ordinary matrix…
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
The main goal of the paper is the discussion of a deeper interaction between matrix theory over polynomial rings over a field and typical methods of commutative algebra and related algebraic geometry. This is intended in the sense of…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
The notion of quantum matrix pairs is defined. These are pairs of matrices with non-commuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are such that products of…
In this note, we define the Burnside ring of a monoid, generalizing the construction for groups. After giving foundational definitions, we characterize transitive M-sets and their automorphisms, then prove a structure theorem for a broad…
The problem of finding a canonical form of complex matrices up to conjugacy with the set of canonical matrices being a union of affine planes in the matrix space is considered. A solution of the problem is given producing a new canonical…
Theoretical and computational frameworks of modern science are dominated by binary structures. This binary bias, seen in the ubiquity of pair-wise networks and formal operations of two arguments in mathematical models, limits our capacity…
Some examples are given of finite dimensional Lie bialgebras whose brackets and cobrackets are determined by pairs of $r$-matrices.
Rings form a bicategory [Rings], with classes of bimodules as horizontal arrows, and bimodule maps as vertical arrows. The notion of Morita equivalence for rings can be translated in terms of bicategories in the following way. Two rings are…
A ring is called a commutator ring if every element is a sum of additive commutators. In this paper we give examples of such rings. In particular, we show that given any ring R, a right R-module N, and a set X, End_R(\bigoplus_X N) and…
The main goal of this article is to introduce BL-rings, i.e., commutative rings whose lattices of ideals can be equipped with a structure of BL-algebra. We obtain a description of such rings, and study the connections between the new class…
An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The…