-clean rings.
near-rings.
Parameterabhängige nichtkommutative Distributionenalgebren
Parametric representations of BiHom-Hopf algebras
The main purpose of the present paper is to study representations of BiHom-Hopf algebras. We first introduce the notion of BiHom-Hopf algebras, and then discuss BiHom-type modules, Yetter-Dinfeld modules and Drinfeld doubles with parameters. We get some new -monoidal categories via the category of BiHom-(co)modules and the category of BiHom-Yetter-Drinfeld modules. Finally, we obtain a center construction type theorem on BiHom-Hopf algebras.
Partial flag varieties and preprojective algebras
Let be a preprojective algebra of type , and let be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories for an injective -module, and we introduce a mutation operation between complete rigid modules in . This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to .
Partial isometries and EP elements in rings with involution.
Partial orders in semigroups and semirings of right quotients.
Path coalgebras of profinite bound quivers, cotensor coalgebras of bound species and locally nilpotent representations
We prove that the study of the category C-Comod of left comodules over a K-coalgebra C reduces to the study of K-linear representations of a quiver with relations if K is an algebraically closed field, and to the study of K-linear representations of a K-species with relations if K is a perfect field. Given a field K and a quiver Q = (Q₀,Q₁), we show that any subcoalgebra C of the path K-coalgebra K◻Q containing is the path coalgebra of a profinite bound quiver (Q,), and the category C-Comod...
PBW-bases of quantum groups.
Peak reductions and waist reflection functors
Perfect Elements in the Free Modular Lattices.
Perfect Modules.
Perfect rings for which the converse of Schur's lemma holds.
If M is a simple module over a ring R then, by the Schur's lemma, the endomorphism ring of M is a division ring. However, the converse of this result does not hold in general, even when R is artinian. In this short note, we consider perfect rings for which the converse assertion is true, and we show that these rings are exactly the primary decomposable ones.
Periodic rings with commuting nilpotents.
Periodic rings with finitely generated underlying group.
Periodicity and representation type of modular Lie algebras.
Permutation Identity Near-RIngs and "Localized" Distributivity Conditions.
Pfaffians, central simple algebras and similtudes.
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...
Piecewise hereditary algebras under field extensions
Let be a finite-dimensional -algebra and be a finite separable field extension. We prove that is derived equivalent to a hereditary algebra if and only if so is .