PBW-bases of quantum groups.
Peak reductions and waist reflection functors
Periodic rings with finitely generated underlying group.
Phantom maps and purity in modular representation theory, I
Let k be a field and G a finite group. By analogy with the theory of phantom maps in topology, a map f : M → ℕ between kG-modules is said to be phantom if its restriction to every finitely generated submodule of M factors through a projective module. We investigate the relationships between the theory of phantom maps, the algebraic theory of purity, and Rickard's idempotent modules. In general, adding one to the pure global dimension of kG gives an upper bound for the number of phantoms we need...
P-injective group rings
A ring is called right P-injective if every homomorphism from a principal right ideal of to can be extended to a homomorphism from to . Let be a ring and a group. Based on a result of Nicholson and Yousif, we prove that the group ring is right P-injective if and only if (a) is right P-injective; (b) is locally finite; and (c) for any finite subgroup of and any principal right ideal of , if , then there exists such that . Similarly, we also obtain equivalent characterizations...
Poincaré duality for - Lie superalgebras
Poisson-Lie groupoids and the contraction procedure
On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures on these...
Polynomial and transformation composition rings.
Polynomial identities in smash products.
Polynomial rings over pseudovaluation rings.
Power Series over Coherent Rings.
Power-cancellation of CW-complexes with few cells.
In this paper we use the fact that the rings of integer matrices have the power-substitution property in order to obtain a power-cancellation property for homotopy types of CW-complexes with one cell in dimensions 0 and 4n and a finite number of cells in dimension 2n.
Precovers
Let be an abstract class (closed under isomorpic copies) of left -modules. In the first part of the paper some sufficient conditions under which is a precover class are given. The next section studies the -precovers which are -covers. In the final part the results obtained are applied to the hereditary torsion theories on the category on left -modules. Especially, several sufficient conditions for the existence of -torsionfree and -torsionfree -injective covers are presented.
Precovers and Goldie’s torsion theory
Recently, Rim and Teply , using the notion of -exact modules, found a necessary condition for the existence of -torsionfree covers with respect to a given hereditary torsion theory for the category -mod of all unitary left -modules over an associative ring with identity. Some relations between -torsionfree and -exact covers have been investigated in . The purpose of this note is to show that if is Goldie’s torsion theory and is a precover class, then is a precover class whenever...
Preradicals and generalizations of - modules. I.
Preradicals and generalizations of - modules. II.
Prescribing endomorphism algebras of -free modules
It is a well-known fact that modules over a commutative ring in general cannot be classified, and it is also well-known that we have to impose severe restrictions on either the ring or on the class of modules to solve this problem. One of the restrictions on the modules comes from freeness assumptions which have been intensively studied in recent decades. Two interesting, distinct but typical examples are the papers by Blass [1] and Eklof [8], both jointly with Shelah. In the first case the authors...
Prescribing endomorphism algebras. The cotorsion-free case
Présentation jordanienne de l'algèbre de Weyl A₂
Let k be a commutative field. For any a,b∈ k, we denote by the deformation of the 2-dimensional Weyl algebra over k associated with the Jordanian Hecke symmetry with parameters a and b. We prove that: (i) any can be embedded in the usual Weyl algebra A₂(k), and (ii) is isomorphic to A₂(k) if and only if a = b.
Primary decomposition of torsion -modules.