Related papers: Singular Ideals over arbitrary fields for the two-…

It is proved that, for each pair (m,n) of non-negative integers, there is a Banach space X for which the group K_0(B(X)) is isomorphic to m copies of the integers and the group K_1(B(X)) is isomorphic to n copies of the integers. Along the…

We give an example of an exact, stably finite, simple. separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably finite, approximately divisible, has real rank…

We construct uncountably many mutually nonisomorphic simple separable stably finite unital exact C$^\ast$-algebras which are not isomorphic to their opposite algebras. In particular, we prove that there are uncountably many possibilities…

Non-commutative Gr\"obner bases of two-sided ideals are not necessarily finite. Motivated by this, we provide a closed-form description of a finite and reduced Gr\"obner bases for the two-sided ideal used in the construction of Wangs…

Let $A_{1} := k [t, \partial ]$ be the first algebra over a field $k$ of characteristic zero. One can associate to each right ideal $I$ of $A_1$ its Stafford subgroup, which is a subgroup of $\Aut_k(A_1)$, the automorphism group of the ring…

Let $\Gamma$ be the unit circle, $A(\Gamma)$ the Wiener algebra of continuous functions whose series of Fourier coefficients are absolutely convergent, and $A^+$ the subalgebra of $A(\Gamma)$ of functions whose negative coefficients are…

We study the relationship between the central ideals and the Jacobson radicals of blocks of group algebras.In particular, we characterize the blocks with the property that the square of the radical is a non-zero central ideal. Moreover, we…

Let $G$ be an (oriented) graph on the vertex set $V = \{ 0, 1,\ldots,n\}$ with root $0$. Postnikov and Shapiro associated a monomial ideal $\mathcal{M}_G$ in the polynomial ring $ R = {\mathbb{K}}[x_1,\ldots,x_n]$ over a field $\mathbb{K}$.…

The Tjurina ideal of a germ of an holomorphic function $f$ is the ideal of $\mathscr{O}_{\mathbbm{C}^n,0}$ - the ring of those germs at $0\in\mathbbm{C}^n$ - generated by $f$ itself and by its partial derivatives. Here it is denoted by…

We give a one-to-one correspondence between ideals in the Steinberg algebra of a Hausdorff ample groupoid $G$, and certain families of ideals in the group algebras of isotropy groups in $G$. This generalises a known ideal correspondence…

In this paper, we compute the exact values of regularity of the quotient rings of the edge ideals associated to multi triangular snake and multi triangular ouroboros snake graphs. Also we compute the exact values of depth, Stanley depth,…

In this paper we study singular integrals on small (that is, measure zero and lower than full dimensional) subsets of metric groups. The main examples of the groups we have in mind are Euclidean spaces and Heisenberg groups. In addition to…

In this paper, we give the definitions of the non-self-adjoint spectral triple and its spectral Einstein functional. We compute the spectral Einstein functional associated with the nonminimal de Rham-Hodge operator on even-dimensional…

A notion of partial ideal for an operator algebra is a weakening the notion of ideal where the defining algebraic conditions are enforced only in the commutative subalgebras. We show that, in a von Neumann algebra, the ultraweakly closed…

We study singular integral operators with kernels that are more singular than standard Calder\'on-Zygmund kernels, but less singular than bi-parameter product Calder\'on-Zygmund kernels. These kernels arise as restrictions to two dimensions…

We provide an infinite series of commutative finite-dimensional Gorenstein local algebras $A_n$ for $n \ge 2$. We give an elementary proof that the maximal ideal of every algebra $A_n$ possesses a one-dimensional subspace that is different…

In this paper, we systematically study spherically symmetric static spacetimes in the framework of Einstein-aether theory, and pay particular attention to the existence of black holes (BHs). In the present studies we first clarify several…

Let G be a finite group and K be a field of characteristic zero. Our purpose is to investigate the ideals of the slice Burnside functor K{\Xi}. It turns out that they are the subfunctors F of K{\Xi} such that for any finite group G, the…

Macaulay's theorem and Fr\"oberg's conjecture deal with the Hilbert function of homogeneous ideals in polynomial rings $S$ over a field $K$. In this short note we present some questions related to variants of Macaulay's theorem and…

Let $(R, \Delta)$ be an odd form algebra. We show that the unitary Steinberg group $\mathrm{StU}(R, \Delta)$ is a crossed module over the odd unitary group $\mathrm U(R, \Delta)$ in two major cases: if the odd form algebra has a free…