Related papers: Primitive ideals of noetherian generalized down-up…

Let $k$ be a field of characteristic $p>0$ and $R$ be a subalgebra of $k[X]=k[x_1,...,x_n]$. Let $J(R)$ be the ideal in $k[X]$ defined by $J(R)\Omega_{k[X]/k}^n=k[X]\Omega_{R/k}^n$. It is shown that if it is a principal ideal then $J(R)^q$…

We classify essential algebras whose irredundant non-refinable covers consist of primal algebras. The proof is obtained by constructing one to one correspondence between such algebras and partial orders on finite sets. Further, we prove…

We introduce the class of principal symmetric ideals, which are ideals generated by the orbit of a single polynomial under the action of the symmetric group. Fixing the degree of the generating polynomial, this class of ideals is…

Primitive cohomology of a Hopf algebra is defined by using a modification of the cobar construction of the underlying coalgebra. Among many of its applications, two classifications are presented. Firstly we classify all non locally PI,…

The study of different types of ideals in non self-adjoint operator algebras has been a topic of recent research. This study focuses on principal ideals in subalgebras of groupoid C*-algebras. An ideal is said to be principal if it is…

Let $G$ be a flat finite-type group scheme over a scheme $S$, and $X$ a noetherian $S$-scheme on which $G$-acts. We define and study $G$-prime and $G$-primary $G$-ideals on $X$ and study their basic properties. In particular, we prove the…

We introduce a notion of generalized homogeneous derivations on graded rings as a natural extension of the homogeneous derivations defined by Kanunnikov. We then define gr-generalized derivations, which preserve the degrees of homogeneous…

We provide primitive recursive bounds for the finite version of Gowers' $c_0$ theorem for both the positive and the general case. We also provide multidimensional versions of these results.

We study the distribution of principal ideals generated by irreducible elements in an algebraic number field.

We show that the full group C$^*$-algebra of the free product of two nontrivial countable amenable discrete groups, where at least one of them has more than two elements, is primitive. We also show that in many cases, this C$^*$-algebra is…

For a general class of non-negative functions defined on integral ideals of number fields, upper bounds are established for their average over the values of certain principal ideals that are associated to irreducible binary forms with…

In this note we study associative dialgebras proving that the most interesting such structures arise precisely when the algebra is not semiprime. In fact the presence of some "perfection" property (simpleness, primitiveness, primeness or…

We provide a complete classification of all algebras of generalised dihedral type, which are natural generalizations of algebras which occurred in the study of blocks with dihedral defect groups. This gives a description by quivers and…

In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.

This paper contains a survey of some ring-theoretic aspects of quantized coordinate rings, with primary focus on the prime and primitive spectra. For these algebras, the overall structure of the prime spectrum is governed by a partition…

A complete classifications, up to isomorphism, of two-dimensional associative and diassociative algebras over any basic field are given.

We introduce the method of calculation of index of Lie algebras that are factors of the unitriangular Lie algebra with respect to ideals spanned by subsets of root vectors.

We classify, up to equivalence, all finite-dimensional simple graded division algebras over the field of real numbers. The grading group is any finite abelian group.

It is shown that any set of nonzero monomial prime ideals can be realized as the stable set of associated prime ideals of a monomial ideal. Moreover, an algorithm is given to compute the stable set of associated prime ideals of a monomial…

The purpose of this paper is to study finiteness conditions on injective hulls of simple modules over Noetherian Down-Up algebras. We will show that the Noetherian Down-Up algebras A(\alpha,\beta,\gamma) which are fully bounded are…