Related papers: Projective indecomposable modules and quivers for …

The separability tensor element of a separable extension of noncommutative rings is an idempotent when viewed in the correct endomorphism ring; so one speaks of a separability idempotent, as one usually does for separable algebras. It is…

Let $\Lambda$ be a basic finite dimensional algebra over an algebraically closed field, with the property that the square of the Jacobson radical $J$ vanishes. We determine the irreducible components of the module variety $\text{Mod}_{\bf…

A classical result of topological algebra states that any compact left topological semigroup has an idempotent. We refine this by showing that any compact left topological left semiring has a common, i.e. additive and multiplicative…

We introduce an infinite family of quiver representation-valued invariants of classical, virtual and surface-knots and links associated to a choice of finite biquandle, commutative unital ring, biquandle module and set of biquandle…

A module over a ring $R$ is pure projective provided it is isomorphic to a direct summand of a direct sum of finitely presented modules. We develop tools for the classification of pure projective modules over commutative noetherian rings.…

The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1)-bundles over quantum real weighted projective spaces are constructed. As the spaces in…

In this note we give an explicit description of the irreducible components of the reduced point varieties of quantum polynomial algebras.

Let $\left( H,R\right) $ be a finite dimensional semisimple and cosemisimple quasi-triangular Hopf algebra over a field $k$. In this paper, we give the structure of irreducible objects of the Yetter-Drinfeld module category ${}…

Recall that an algebraic module is a KG-module that satisfies a polynomial with integer coefficients, with addition and multiplication given by direct sum and tensor product. In this article we prove that if L is a component of the (stable)…

Let $Q$ be a finite quiver and $\Lambda$ be the radical square zero algebra of $Q$ over a field. We give a full and dense functor from the category of reduced differential projective modules over $\Lambda$ to the category of representations…

In this article, the projectivity of finitely generated flat modules of a commutative ring are studied from a topological point of view. Then various interesting results are obtained. For instance, it is shown that if a ring has either a…

The geometric and algebraic theory of monomial ideals and multigraded modules is initiated over real-exponent polynomial rings and, more generally, monoid algebras for real polyhedral cones. The main results include the generalization of…

For the algebra $\mI_1= K<x, \frac{d}{dx}, \int>$ of polynomial integro-differential operators over a field $K$ of characteristic zero, a classification of simple modules is given. It is proved that $\mI_1$ is a left and right coherent…

We classify real 6-dimensional nilpotent Lie algebras for which the corresponding Lie group has a left-invariant complex structure, and estimate the dimensions of moduli spaces of such structures.

Many rings and algebras arising in quantum mechanics, algebraic analysis, and non-commutative algebraic geometry can be interpreted as skew PBW (Poincar\'e-Birkhoff-Witt) extensions. In the present paper we study two aspects of these…

Let R be an affine algebra of dimension n \geq 3 over an algebraically closed field k. Suppose char k =0 or char k =p \geq n. Let g,f_1,...,f_r be a R-regular sequence and A=R[f_1/g,...,f_r/g]. Let P be a projective A-module of rank n-1…

A general method for constructing logarithmic modules in vertex operator algebra theory is presented. By utilizing this approach, we give explicit vertex operator construction of certain indecomposable and logarithmic modules for the…

Given a quiver $Q$, a formal potential is called analytic if its coefficients are bounded by the terms of a geometric series. As shown by Toda, the potentials appearing in the deformation theory of complexes of coherent sheaves on complex…

It is proved that, for a left hereditary ring, an arbitrary left module has a representation in the form of the direct sum of a stable left module and indecomposable projective left modules (if and only if an arbitrary left module has a…

We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…