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P -clean rings.

Chen, Weixing (2006)

International Journal of Mathematics and Mathematical Sciences

P ( r , m ) near-rings.

Balakrishnan, R., Suryanarayanan, S. (2000)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Parametric representations of BiHom-Hopf algebras

Xiaohui Zhang, Wei Wang, Juzhen Chen (2024)

Czechoslovak Mathematical Journal

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 n -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

Christof Geiß, Bernard Leclerc, Jan Schröer (2008)

Annales de l’institut Fourier

Let Λ be a preprojective algebra of type A , D , E , and let G be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories Sub Q for Q an injective Λ -module, and we introduce a mutation operation between complete rigid modules in Sub Q . This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to  G .

Path coalgebras of profinite bound quivers, cotensor coalgebras of bound species and locally nilpotent representations

Daniel Simson (2007)

Colloquium Mathematicae

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 K Q K Q is the path coalgebra K ( Q , ) of a profinite bound quiver (Q,), and the category C-Comod...

Perfect rings for which the converse of Schur's lemma holds.

Abdelfattah Haily, Mostafa Alaoui (2001)

Publicacions Matemàtiques

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.

Phantom maps and purity in modular representation theory, I

D. Benson, G. Gnacadja (1999)

Fundamenta Mathematicae

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

Jie Li (2021)

Czechoslovak Mathematical Journal

Let A be a finite-dimensional k -algebra and K / k be a finite separable field extension. We prove that A is derived equivalent to a hereditary algebra if and only if so is A k K .

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