Abstract
We introduce the concept of an object with the (finite) exchange property in an arbitrary Grothendieck category, and we present the basic properties of such an object. Applications are given for categories of graded modules and for categories of comodules over a coalgebra. Among other results, it is proved that an arbitrary coalgebra 𝒞 over a field has the finite exchange property.
Original language | English |
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Pages (from-to) | 1433-1442 |
Number of pages | 10 |
Journal | Communications in Algebra |
Volume | 44 |
Issue number | 4 |
DOIs | |
Publication status | Published - Apr 2 2016 |
Keywords
- Coalgebra
- Exchange property
- Graded module
- Grothendieck category
- Suitable ring
ASJC Scopus subject areas
- Algebra and Number Theory