EVERY POSET APPEARS AS THE ATOM SPECTRUM OF SOME GROTHENDIECK CATEGORY (Combinatorial Representation Theory and Related ...
EVERY POSET APPEARS AS THE ATOM SPECTRUM OF SOME GROTHENDIECK CATEGORY (Combinatorial Representation Theory and Related ...
EVERY POSET APPEARS AS THE ATOM SPECTRUM OF SOME GROTHENDIECK CATEGORY (Combinatorial Representation Theory and Related ...
Covering theory for linear categories with application to derived categories
Published in Journal of Algebra
Covering theory for linear categories with application to derived categories
Published in Journal of Algebra
We extend the Galois covering theory introduced by Bongartz–Gabriel for skeletal linear categories to general linear categories. We show that a Galois covering between Krull–Schmidt categories preserves irreducible morphisms and almost splits sequences. Specializing to derived categories, we study when a Galois covering between locally bounded line...
Flat endofinite modules, prime ideals, and duality
Published in Journal of Algebra
On the commutativity of the Clifford and “extension of scalars” functors
Published in Topology and its Applications
On the commutativity of the Clifford and “extension of scalars” functors
Published in Topology and its Applications
We introduce sheaves of A-modules of fractions (or just A-modules of fractions), on a topological space X, with denominator a monoid-subsheaf S of A; as aside worth noting, we remark (Theorem 2.4) that there is an isomorphism between the functors S−1 and (S−1A)⊗_. Moreover, we discuss the classical problem related to the commutativity of the functo...
Flat endofinite modules, prime ideals, and duality
Published in Journal of Algebra
Bijective correspondences are established between endofinite injective left modules, endofinite flat right modules, finite collections of minimal noetherian prime ideals, normalized rank functions on left ideals and characters. Endofinite flat modules are identified as flat covers of modules associated to a minimal noetherian prime ideal, while end...
Hereditary rings with countably generated cotorsion envelope
Published in Journal of Algebra
