Related papers: Primitive quantales
We classify the primitive ideals of generalized down-up algebras
Let $R$ be a commutative ring with identity. For an $R$-module $M$, the notion of strongly prime submodule of $M$ is defined. It is shown that this notion of prime submodule inherits most of the essential properties of the usual notion of…
We introduce the notions of quantum characteristic and quantum flatness for arbitrary rings. More generally, we develop the theory of quantum integers in a ring and show that the hypothesis of quantum flatness together with positive quantum…
Let $k$ be a field and let $R$ be a countable dimensional prime von Neumann regular $k$-algebra. We show that $R$ is primitive, answering a special case of a question of Kaplansky.
A famous result due to I. M. Isaacs states that if a commutative ring $R$ has the property that every prime ideal is principal, then every ideal of $R$ is principal. This motivates ring theorists to study commutative rings for which every…
We introduce a lattice structure as a generalization of meet-continuous lattices and quantales. We develop a point-free approach to these new lattices and apply these results to $R$-modules. In particular, we give the module counterpart of…
The aim of this paper is to study the primitive ideals of Novikov algebras. In terms of modular maximal right ideals, a characterization of the primitive ideals of a Novikov algebra has been obtained. We prove a Chevalley-Jacobson…
We consider primitive divisors of terms of integer sequences defined by quadratic polynomials. Apart from some small counterexamples, when a term has a primitive divisor, that primitive divisor is unique. It seems likely that the number of…
It is proved that any supersimple field has trivial Brauer group, and more generally that any supersimple division ring is commutative. As prerequisites we prove several results about generic types in groups and fields whose theory is…
In this paper, we introduce the concepts of strongly 2-absorbing primary ideals (resp., submodules) and strongly 2-absorbing ideals (resp., submodules) as generalizations of strongly prime ideals. Furthermore, we investigate some basic…
For a commutative ring R we investigate the property that the sets of minimal primes of finitely generated ideals of R is always finite. We prove this property passes to polynomial ring extensions (in an arbitrary number of variables) over…
The paper sets out a primitive ontology of the natural world in terms of primitive stuff, that is, stuff that has as such no physical properties at all, but that is not a bare substratum either, being individuated by metrical relations. We…
We extend two well-known results on primitive ideals in enveloping algebras of semisimple Lie algebras, the `Irreducibility theorem' and `Duflo theorem', to much wider classes of algebras. Our general version of Irreducibility theorem says…
We prove that an integral Jacobson radical ring is always nil, which extends a well known result from algebras over fields to rings. As a consequence we show that if every element x of a ring R is a zero of some polynomial p_x with integer…
We characterize several properties of core quandles in terms of the properties of their underlying groups. Specifically, we characterize connected cores providing an answer to an open question in \cite{saito} and present a standard…
In this paper we characterize the projective modules over an arbitrary quantale, and then we apply such a characterization in order to define the K_0 group of a quantale. Then we study congruences of quantales and quantale modules by means…
In this study, we introduce the concept of "uniformly 2-absorbing primary ideals" of commutative rings, which imposes a certain boundedness condition on the usual notion of 2-absorbing primary ideals of commutative rings. Then we…
We show that every proper, dense ideal in a C*-algebra is contained in a prime ideal. It follows that a subset generates a C*-algebra as a not necessarily closed ideal if and only if it is not contained in any prime ideal. This allows us to…
Recently, the Mac\'ias topology has been generalized over integral domains that are not fields, to furnish a topological proof of the infinitude of prime elements under the assumption that the set of units is finite or not open. In this…
The main theorem (2.2) consists in two characterizations of isomorphisms of factorial domains in terms of prime or primary rings elements, and unramified, flat or weakly injective affine schemes morphisms. In order to apply this theorem to…