A note on three types of quasisymmetric functions.
A Note On Units And Divisors Of Zero In Group Rings
A Priddy-type Koszulness criterion for non-locally finite algebras
A celebrated result by S. Priddy states the Koszulness of any locally finite homogeneous PBW-algebra, i.e. a homogeneous graded algebra having a Poincaré-Birkhoff-Witt basis. We find sufficient conditions for a non-locally finite homogeneous PBW-algebra to be Koszul, which allows us to completely determine the cohomology of the universal Steenrod algebra at any prime.
A property of the degree filtration of polynomial functors.
A Reduction Theorem for the Primitivity of Tensor Products.
A remark on decomposable modules.
A remark on differential operator algebras and an equivalence of categories
A representation theorem for certain Boolean lattices.
Let R be an associative ring with 1 and R-tors the somplete Brouwerian lattice of all hereditary torsion theories on the category of left R-modules. A well known result asserts that R is a left semiartinian ring iff R-tors is a complete atomic Boolean lattice. In this note we prove that if L is a complete atomic Boolean lattice then there exists a left semiartinian ring R such that L is lattice-isomorphic to R-tors.
A representation theorem for Chain rings
A ring A is called a chain ring if it is a local, both sided artinian, principal ideal ring. Let R be a commutative chain ring. Let A be a faithful R-algebra which is a chain ring such that Ā = A/J(A) is a separable field extension of R̅ = R/J(R). It follows from a recent result by Alkhamees and Singh that A has a commutative R-subalgebra R₀ which is a chain ring such that A = R₀ + J(A) and R₀ ∩ J(A) = J(R₀) = J(R)R₀. The structure of A in terms of a skew polynomial ring over R₀ is determined.
A semigroup approach to wreath-product extensions of Solomon's descent algebras.
A splitting theorem for ℱ-products
A structure sheaf on the projective spectrum of a graded fully bounded Noetherian ring.
A subclass of strongly clean rings
In this paper, we introduce a subclass of strongly clean rings. Let be a ring with identity, be the Jacobson radical of , and let denote the set of all elements of which are nilpotent in . An element is called very -clean provided that there exists an idempotent such that and or is an element of . A ring is said to be very -clean in case every element in is very -clean. We prove that every very -clean ring is strongly -rad clean and has stable range one. It is shown...
A Survey of Rings Generated by Units
This article presents a brief survey of the work done on rings generated by their units.
A unified approach to the Armendariz property of polynomial rings and power series rings
A ring R is called Armendariz (resp., Armendariz of power series type) if, whenever in R[x] (resp., in R[[x]]), then for all i and j. This paper deals with a unified generalization of the two concepts (see Definition 2). Some known results on Armendariz rings are extended to this more general situation and new results are obtained as consequences. For instance, it is proved that a ring R is Armendariz of power series type iff the same is true of R[[x]]. For an injective endomorphism σ of a ring...
A weaker form of Baer’s splitting problem for torsion theories
Abelian modules.
Abelian p-adic Group Rings.
Actions of parabolic subgroups in GL_n on unipotent normal subgroups and quasi-hereditary algebras
Let R be a parabolic subgroup in . It acts on its unipotent radical and on any unipotent normal subgroup U via conjugation. Let Λ be the path algebra of a directed Dynkin quiver of type with t vertices and B a subbimodule of the radical of Λ viewed as a Λ-bimodule. Each parabolic subgroup R is the group of automorphisms of an algebra Λ(d), which is Morita equivalent to Λ. The action of R on U can be described using matrices over the bimodule B. The advantage of this description is that each...
Actions of the additive group on certain noncommutative deformations of the plane
We connect the theorems of Rentschler [rR68] and Dixmier [jD68] on locally nilpotent derivations and automorphisms of the polynomial ring and of the Weyl algebra , both over a field of characteristic zero, by establishing the same type of results for the family of algebras where is an arbitrary polynomial in . In the second part of the paper we consider a field of prime characteristic and study comodule algebra structures on . We also compute the Makar-Limanov invariant of absolute constants...