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A representation theorem for certain Boolean lattices.

José Ríos Montes (1988)

Publicacions Matemàtiques

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.

Compact corigid objects in triangulated categories and co-t-structures

David Pauksztello (2008)

Open Mathematics

In the work of Hoshino, Kato and Miyachi, [11], the authors look at t-structures induced by a compact object, C , of a triangulated category, 𝒯 , which is rigid in the sense of Iyama and Yoshino, [12]. Hoshino, Kato and Miyachi show that such an object yields a non-degenerate t-structure on 𝒯 whose heart is equivalent to Mod(End( C )op). Rigid objects in a triangulated category can the thought of as behaving like chain differential graded algebras (DGAs). Analogously, looking at objects which behave...

Composition of preradicals

Ladislav Bican, Pavel Jambor, Tomáš Kepka, Petr Němec (1974)

Commentationes Mathematicae Universitatis Carolinae

Costable rings

Tomáš Kepka (1974)

Commentationes Mathematicae Universitatis Carolinae

Finitely silting comodules in quasi-finite comodule category

Qianqian Yuan, Hailou Yao (2023)

Czechoslovak Mathematical Journal

We introduce the notions of silting comodules and finitely silting comodules in quasi-finite category, and study some properties of them. We investigate the torsion pair and dualities which are related to finitely silting comodules, and give the equivalences among silting comodules, finitely silting comodules, tilting comodules and finitely tilting comodules.

Gabriel filters in Grothendieck categories.

Ana Jeremías López, María Purificación López López, Emilio Villanueva Nóvoa (1992)

Publicacions Matemàtiques

In [1] it is proved that one must take care trying to copy results from the case of modules to an arbitrary Grothendieck category in order to describe a hereditary torsion theory in terms of filters of a generator. By the other side, we usually have for a Grothendick category an infinite family of generators {Gi; i ∈ I} and, although each Gi has good properties the generator G = ⊕i ∈ I Gi is not easy to handle (for instance in categories like graded modules). In this paper the authors obtain a bijective...

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