References Page 1 References [1] S. Abhyankar, S. Wiegand, On the compositum of two power
series rings, Proc. Amer. Math. Soc. 112 (1991), 629 – 636. [2] U. Albrecht, Endomorphism …

It is possible to associate a topological space to the category of modules over any ring. This
space, the Ziegler spectrum, is based on the indecomposable pure-injective modules …

Various classification theorems of thick subcategories of a triangulated category have been
obtained in many areas of mathematics. In this paper, as a higher-dimensional version of the …

We classify all tilting and cotilting classes over commutative noetherian rings in terms of
descending sequences of specialization closed subsets of the Zariski spectrum …

For an arbitrary finite dimensional algebra $\Lambda $, we prove that any wide subcategory
of $\mathsf {mod}\Lambda $ satisfying a certain finiteness condition is $\theta $-semistable …

In this paper, we introduce the atom spectrum of an abelian category as a topological space
consisting of all the equivalence classes of monoform objects. In terms of the atom spectrum …

In 1962, P. Gabriel showed the existence of a lattice isomorphism between the set of Serre
subcategories of the category consisting of finitely generated modules and the set of …

We classify certain resolving subcategories of finitely generated modules over a
commutative noetherian ring R by using integer-valued functions on SpecR. As an …

For a commutative noetherian ring A, we compare the support of a complex of A-modules
with the support of its cohomology. This leads to a classification of all full subcategories of A …

There are well-known constructions relating ring epimorphisms and tilting modules. The new
notion of silting module provides a wider framework for studying this interplay. To every …