An analogue of holonomic -modules on smooth varieties in positive characteristics.
An analogue of the Duistermaat-van der Kallen theorem for group algebras
Let G be a group, R an integral domain, and V G the R-subspace of the group algebra R[G] consisting of all the elements of R[G] whose coefficient of the identity element 1G of G is equal to zero. Motivated by the Mathieu conjecture [Mathieu O., Some conjectures about invariant theory and their applications, In: Algèbre non Commutative, Groupes Quantiques et Invariants, Reims, June 26–30, 1995, Sémin. Congr., 2, Société Mathématique de France, Paris, 1997, 263–279], the Duistermaat-van der Kallen...
An Application of a Theorem of Ziegler.
An application of Zassenhaus' unit theorem
An approach to Hopf algebras via Frobenius coordinates.
An approximation theorem for Dubrovin valuation rings.
An axiomatic approach to homological dimension.
An elementary exact sequence of modules with an application to tiled orders
Let m ≥ 2 be an integer. By using m submodules of a given module, we construct a certain exact sequence, which is a well known short exact sequence when m = 2. As an application, we compute a minimal projective resolution of the Jacobson radical of a tiled order.
An elementary note on group-rings.
An Elementary Treatise on Quaternions [Book]
An embedding theorem for free associative algebras.
An example of two von Neumann regular rings with nonisomorphic Monta equivalent multiplicative semigroups.
An explicit construction for the Happel functor
An easy explicit construction is given for a full and faithful functor from the bounded derived category of modules over an associative algebra A to the stable category of the repetitive algebra of A. This construction simplifies the one given by Happel.
An extension of Zassenhaus' theorem on endomorphism rings
Let R be a ring with identity such that R⁺, the additive group of R, is torsion-free. If there is some R-module M such that and , we call R a Zassenhaus ring. Hans Zassenhaus showed in 1967 that whenever R⁺ is free of finite rank, then R is a Zassenhaus ring. We will show that if R⁺ is free of countable rank and each element of R is algebraic over ℚ, then R is a Zassenhaus ring. We will give an example showing that this restriction on R is needed. Moreover, we will show that a ring due to A....
An extension theorem and a new construction of Dickson near-fields.
An extension theorem and a new construction of Dickson near-fields. (Short Communications).
An homotopy formula for the Hochschild cohomology
An ideal-based zero-divisor graph of direct products of commutative rings
In this paper, specifically, we look at the preservation of the diameter and girth of the zero-divisor graph with respect to an ideal of a commutative ring when extending to a finite direct product of commutative rings.
An identity in Rota-Baxter algebras.
An identity on partial generalized automorphisms of prime rings