Related papers: Idempotent generated algebras and Boolean powers o…

Let $\Lambda$ be an artin algebra and $\mathfrak{A}$ a two-sided idempotent ideal of $\Lambda$, that is, $\mathfrak{A}$ is the trace of a projective $\Lambda$-module $P$ in $\Lambda$. We consider the categories of finitely generated modules…

Let G be a simple complex algebraic group and let K be a reductive subgroup of G such that the coordinate ring of G/K is a multiplicity free G-module. We consider the G-algebra structure of C[G/K], and study the decomposition into…

We proved in a previous article that the bar complex of an E-infinity algebra inherits a natural E-infinity algebra structure. As a consequence, a well-defined iterated bar construction B^n(A) can be associated to any algebra over an…

For $R_1,R_2,R_3,\dots$ a family of non isomorphic rings (or algebras) having each only 2 idempotents ($1$ and $0$), we classify up to isomorphism the rings (or algebras) obtained by taking products of powers of the different $R_i$. We show…

In this paper, we study module theoretic definitions of the Baer and related ring concepts. We say a module is s.Baer if the right annihilator of a nonempty subset of the module is generated by an idempotent in the ring. We show that s.Baer…

We consider commutative C* -algebras of Toeplitz operators in the weighted Bergman space on the unit ball in $\mathbb{C}^{\mathbf{n}}$. For the algebras of elliptic type we find a new representation, namely as the algebra of operators which…

We recall the derived subalgebra of a BCK-algebra, and use this to define the derived ideal. Using the derived ideal, we show that the category of commutative BCK-algebras is a reflective subcategory of the category of BCK-algebras. After…

We consider a complete filtered Rota-Baxter algebra of weight $\lambda$ over a commutative ring. Finding the unique solution of a non-homogeneous linear algebraic equation in this algebra, we generalize Spitzer's identity in both…

For an effect algebra $A$, we examine the category of all morphisms from finite Boolean algebras into $A$. This category can be described as a category of elements of a presheaf $R(A)$ on the category of finite Boolean algebras. We prove…

Cohomological genus-0 Gromov-Witten invariants of a given target space can be encoded by the "descendant potential," a generating function defined on the space of power series in one variable with coefficients in the cohomology space of the…

We show that the cohomology ring of a quiver Grassmannian asssociated with a rigid quiver representation has property (S): there is no odd cohomology and the cycle map is an isomorphism; moreover, its Chow ring admits explicit generators…

In this paper we investigate a multi-parameter deformation $\mathfrak{B}_{r,s}^n(a,\lambda,\delta)$ of the walled Brauer algebra which was previously introduced by Leduc (\cite{leduc}). We construct an integral basis of…

Let $k$ be a field and let $R$ be a left noetherian $k$-algebra. The algebra $R$ satisfies the Dixmier-Moeglin equivalence if the annihilators of irreducible representations are precisely those prime ideals that are locally closed in the…

Segal's Gamma-rings provide a natural framework for absolute algebraic geometry. We use Almkvist's global Witt construction to explore the relation with J. Borger F1-geometry and compute the Witt functor-ring of Almkvist for the simplest…

Let $S=K[x_1,\dots,x_n]$ be the polynomial ring over a field $K$, and let $I\subset S$ be a monomial ideal. In this paper, we introduce the $i$th \textit{homological shift algebras}…

A commutative residuated lattice A is said to be subidempotent if the lower bounds of its neutral element e are idempotent (in which case they naturally constitute a Brouwerian algebra A*). It is proved here that epimorphisms are surjective…

We realize (via an explicit isomorphism) the walled Brauer algebra for an arbitrary integral parameter delta as an idempotent truncation of a level two cyclotomic degenerate affine walled Brauer algebra. The latter arises naturally in Lie…

Let $S$ be a partial groupoid, that is, a set with a partial binary operation. An $S$-graded ring $R$ is said to be graded von Neumann regular if $x\in xRx$ for every homogeneous element $x\in R.$ Under the assumption that $S$ is…

This paper introduces an analogue of the Solomon descent algebra for the complex reflection groups of type $G(r,1,n)$. As with the Solomon descent algebra, our algebra has a basis given by sums of `distinguished' coset representatives for…

We study the closed algebra B_I(G) generated by the idempotents in the Fourier-Stieltjes algebra of a locally compact group G. We show that it is a regular Banach algebra with computable spectrum G^I, which we call the idempotent…