Cohomological dimensions of specialization-closed subsets and subcategories of modules
Let $ R $ be a commutative noetherian ring. In this paper, we study specialization-closed
subsets of $\mathrm {Spec} R $. More precisely, we first characterize the specialization …
subsets of $\mathrm {Spec} R $. More precisely, we first characterize the specialization …
[PDF][PDF] The pure spectrum of a PF-ring
H Al-Ezeh - Commentarii Mathematici Universitatis Sancti Pauli, 1988 - rikkyo.repo.nii.ac.jp
All rings considered in this paper are commutative with unity. A ring R is called a PF-ring if
every principal ideal a R is a flat R-module, and it is called a PP-ring if every principal ideal a …
every principal ideal a R is a flat R-module, and it is called a PP-ring if every principal ideal a …
On prime spectrums of commutative rings
D Lu, W Yu - Communications in Algebra®, 2006 - Taylor & Francis
We show that π-regular rings and clean rings can be completely characterized by
topological properties of their prime spectrums respectively. In addition, we give some …
topological properties of their prime spectrums respectively. In addition, we give some …
Abstractly constructed prime spectra
A Facchini, CA Finocchiaro, G Janelidze - Algebra universalis, 2022 - Springer
The main purpose of this paper is a wide generalization of one of the results abstract
algebraic geometry begins with, namely of the fact that the prime spectrum Spec (R) Spec …
algebraic geometry begins with, namely of the fact that the prime spectrum Spec (R) Spec …
Neat and coneat submodules of modules over commutative rings
S Crivei - Bulletin of the Australian Mathematical Society, 2014 - cambridge.org
We prove that neat and coneat submodules of a module coincide when is a commutative
ring such that every maximal ideal is principal, extending a recent result by Fuchs. We …
ring such that every maximal ideal is principal, extending a recent result by Fuchs. We …
[PDF][PDF] On the decomposition of modules
A Dress - 1969 - projecteuclid.org
THEOREM 1. Assumptions.(i) N is finitely presented as A-left-module, EndA (N) finitely
generated as R-module and M a direct summand in a direct sum of finitely presented A …
generated as R-module and M a direct summand in a direct sum of finitely presented A …
[PDF][PDF] The spectrum of a finite dimensional algebra
CM Ringel - Ring theory. Proceedings of the 1978 Antwerp …, 1979 - core.ac.uk
A right rnodule M over a ring R is said to have a unimodular element (UME) if there exists ue
M such that uR is a direct summand of M canonically isomorphic to R., Thus, M has a UME iff …
M such that uR is a direct summand of M canonically isomorphic to R., Thus, M has a UME iff …
Real spectra of complete local rings
ME Alonso, C Andradas - manuscripta mathematica, 1987 - Springer
We Show that:(a) closures of a constructible subsets of real spectrum (Spec r A) of complete
noetherian local ring A with formally real residue field R are constructible.(b) The connected …
noetherian local ring A with formally real residue field R are constructible.(b) The connected …
[PDF][PDF] Prime ideal structure in commutative rings
M Hochster - Transactions of the American Mathematical Society, 1969 - ams.org
0. Introduction. Let<€ be the category of commutative rings with unit, and regard Spec (as in
[1]) as a contra variant functor from# to 3~, the category of topological spaces and …
[1]) as a contra variant functor from# to 3~, the category of topological spaces and …
[PDF][PDF] S-modules and symmetric spectra
S Schwede - Mathematische Annalen, 2001 - math.uni-bonn.de
Stable homotopy theory studies the homotopy category of spectra. This category has a
symmetric monoidal smash product which allows the definition of ring spectra 'up to …
symmetric monoidal smash product which allows the definition of ring spectra 'up to …