The minus partial order linear algebraic methods have proven to be useful in the study of complex matrices. This paper extends study of minus partial orders to general rings. It is shown that the condition a < b, where < is the minus partial order, defines two triples of orthogonal idempotents, and thus, a decomposition of a ring into a direct sum of abelian groups. Hence, several well-known re...

In this note we study dual coalgebras of algebras over arbitrary (noetherian) commutative rings. We present and study a generalized notion of coreflexive comodules and use the results obtained for them to characterize the so called coreflexive coalgebras. Our approach in this note is an algebraically topological one. Introduction The concept of coreflexive coalgebras was studied, in the case of...

Let k be a field. We prove that any polynomial ring over k is a Kadison algebra if and only if k is infinite. Moreover, we present some new examples of Kadison algebras and examples of algebras which are not Kadison algebras.

Various algebraic structures in geometry and group theory have appeared to be governed by certain universal rings. Examples include: the cohomology rings of Hilbert schemes of points on projective surfaces and quasiprojective surfaces; the Chen-Ruan orbifold cohomology rings of the symmetric products; the class algebras of wreath products, as well as their associated graded algebras with respec...

We prove a Nullstellensatz for the ring of polynomial functions in n non-commuting variables over Hamilton's real quaternions. also characterize generalized identities which hold quaternions, and more generally, any division algebra .

Linear operators preserving the direct sum of polynomial rings P(m)⊕P(n) are constructed. In the case |m − n| = 1 they correspond to atypical representations of the superalgebra osp(2,2). For |m − n| = 2 the generic, finite dimensional representations of the superalgebra q(2) are recovered. Examples of Hamiltonians possessing such a hidden algebra are analyzed. PACS numbers: 02.20.Sv, 03.65.Fd ...

Abstract Free algebras are always free as modules over the base ring in classical algebra. In equivariant algebra, incomplete Tambara functors play role of and Mackey modules. Surprisingly, often fail to be functors. this paper, we determine for all finite groups conditions under which a functor is functor. For solvable groups, show that flat precisely when these hold. Our results imply almost ...

This article is divided into two parts. In the first part we work over a field k and prove that Frobenius space associated to algebra generated as left A-module by coproduct. particular, dimension coincides with of algebra. second commutative ring We introduce concept nearly algebras in this context construct solutions quantum Yang-Baxter equation starting from elements space. Also, give an alt...

This paper is a survey of natural questions (with few answers) arising when one wants to study algebraic properties of real numbers, i.e., properties of real numbers w.r.t. {+, −, ×, >, ≥} in a constructive setting. Introduction This paper is a survey of natural questions (with few answers) arising when one wants to study algebraic properties of real numbers, i.e., properties of real numbers w....

LetW be a finite dimensional representation of a linearly reductive group G over a field k. Motivated by their work on classical rings of invariants, Levasseur and Stafford asked whether the ring of invariants under G of the symmetric algebra of W has a simple ring of differential operators. In this paper, we show that this is true in prime characteristic. Indeed, if R is a graded subring of a ...