Related papers: Noncommutative complete intersections and matrix i…
Several generalizations of a commutative ring that is a graded complete intersection are proposed for a noncommutative graded $k$-algebra; these notions are justified by examples from noncommutative invariant theory.
In recent work of T. Cassidy and the author, a notion of complete intersection was defined for (non-commutative) regular skew polynomial rings, defining it using both algebraic and geometric tools, where the commutative definition is a…
Let $R$ be a positively graded algebra over a field. We say that $R$ is Hilbert-cyclotomic if the numerator of its reduced Hilbert series has all of its roots on the unit circle. Such rings arise naturally in commutative algebra, numerical…
We study associative graded algebras which have a ``complete flag'' of cyclic modules with linear free resolutions, i.e., algebras over which there is a cyclic Koszul module with every admissible number of relations (from zero up to the…
Inspired by the commutator and anticommutator algebras derived from algebras graded by groups, we introduce noncommutatively graded algebras. We generalize various classical graded results to the noncommutatively graded situation concerning…
We study the Hilbert function and the graded Betti numbers of almost complete intersection artinian algebras. We show that that every Hilbert function of a complete intersection artinian algebra is the Hilbert function of an almost complete…
In this paper we show that acyclic $n$-slice algebras are exactly acyclic $n$-hereditary algebras whose $(n+1)$-preprojective algebras are $(q+1,n+1)$-Koszul. We also list the equivalent triangulated categories arising from the algebra…
We investigate relations between the properties of an algebra and its varieties of finite-dimensional module structures, on the example of the Jordan plane $R=k<x,y>/ (xy-yx-y^2)$. Complete description of irreducible components of the…
We investigate compatibility of gradings for an almost Koszul or Koszul algebra $R$ that is also the higher preprojective algebra $\Pi_{n+1}(A)$ of an $n$-hereditary algebra $A$. For an $n$-representation finite algebra $A$, we show that…
In this short note, we simply collect some known results about representing algebraic cycles by various kind of "nice" (e.g. smooth, local complete intersection, products of local complete intersection) algebraic cycles, up to rational…
We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the…
Any finite-dimensional commutative (associative) graded algebra with all nonzero homogeneous subspaces one-dimensional is defined by a symmetric coefficient matrix. This algebraic structure gives a basic kind of $A$-graded algebras…
The Hochschild and (cotriple) cyclic homologies of crossed modules of (not-necessarily-unital) associative algebras are investigated. Wodzicki's excision theorem is extended for inclusion crossed modules in the category of crossed modules…
We construct some irreducible representations of the Leavitt path algebra of an arbitrary quiver. The constructed representations are associated to certain algebraic branching systems. For a row-finite quiver, we classify algebraic…
We call a graded connected algebra $R$ effectively coherent, if for every linear equation over $R$ with homogeneous coefficients of degrees at most $d$, the degrees of generators of its module of solutions are bounded by some function…
Throughout this abstruct $A$ will denote a noetherian commutative ring of dimension $n$. The paper has two parts. Among the interesting results in Part-1 are the following: 1) {\it suppose that $f_1, f_2, ..., f_r$ (with $r \leq n$) is a…
We study non-commutative real algebraic geometry for a unital associative *-algebra A viewing the points as pairs ({\pi},v) where {\pi} is an unbounded *-representation of A on an inner product space which contains the vector v. We first…
Let n be a positive integer, and let R be a finitely presented (but not necessarily finite dimensional) associative algebra over a computable field. We examine algorithmic tests for deciding (1) if every n-dimensional representation of R is…
In present work, we find a class of Lie algebras, which are defined from the symmetrizable generalized intersection matrices. However, such algebras are different from generalized intersection matrix algebras and intersection matrix…
By studying NIM-representations we show that the Fibonacci category and its tensor powers are completely anisotropic; that is, they do not have any non-trivial separable commutative ribbon algebras. As an application we deduce that a chiral…