[PDF][PDF] The category of s-unital modules
H Komatsu - Mathematical Journal of Okayama University, 1986 - ousar.lib.okayama-u.ac.jp
The category of unital modules over a ring with identity element is characterized as a
cocomplete abelian category with a progenerator. More generally, every cocomplete abelian …
cocomplete abelian category with a progenerator. More generally, every cocomplete abelian …
A ring theoretical proof in a factor category of indecomposable modules
M Harada - Journal of the Mathematical Society of Japan, 1976 - jstage.jst.go.jp
We have widely extended the Krull-Remak-Schmidt-Azumaya's theorem in [4],[5],[6],[7],[8]
and [11] and succeeded to prove some of main theorems by virtue of the theory of category …
and [11] and succeeded to prove some of main theorems by virtue of the theory of category …
Auslander's formula for contravariantly finite subcategories
J Asadollahi, R Hafezi, MH Keshavarz - Journal of the Mathematical …, 2021 - jstage.jst.go.jp
Let A be a right coherent ring and X be a contravariantly finite subcategory of mod-A
containing projectives. In this paper, we construct a recollement of abelian categories (mod0 …
containing projectives. In this paper, we construct a recollement of abelian categories (mod0 …
Rings having a Morita-like equivalence
JL Garcia, L Marín - Communications in Algebra, 1999 - Taylor & Francis
The notion of Morita-like equivalence has been introduced by Xu, Shum and Turner-Smith in
[13]. Their definition extends the usual Morita equivalence for unital rings to a wider subclass …
[13]. Their definition extends the usual Morita equivalence for unital rings to a wider subclass …
[PDF][PDF] Endomorphism rings and category equivalences
JL Garcia, M Saorin - Journal of Algebra, 1989 - core.ac.uk
The use of category equivalences for the study of endomorphism rings stems from the Morita
theorem. In a sense, this theorem can be viewed as stating that if P is a finitely generated …
theorem. In a sense, this theorem can be viewed as stating that if P is a finitely generated …
Characterizations of Morita-like equivalences for right XST-rings
B Ouyang, L Zhou, W Tong - Algebra Colloquium, 2007 - World Scientific
The notion of xst-rings was introduced by García and Marín in 1999. In this paper, we
characterize Morita-like equivalences for right xst-rings, obtain the universal theory of Morita …
characterize Morita-like equivalences for right xst-rings, obtain the universal theory of Morita …
A note on cogenerators in the category of modules
Y Kawada - Proceedings of the Japan Academy, 1972 - jstage.jst.go.jp
Let A, be a ring with identity and AW a cogenerator in the category of unitary, left A-modules,
and denote by B= End (AW) the endomorphism ring of; AW. Then W is regarded as an AB …
and denote by B= End (AW) the endomorphism ring of; AW. Then W is regarded as an AB …
Faithfully exact functors and their applications to projective modules and injective modules
T Ishikawa - Nagoya Mathematical Journal, 1964 - cambridge.org
The aim of this paper is to study a property of a special kind of exact functors and give some
applications to projective modules and injective modules. In section 1 we introduce the …
applications to projective modules and injective modules. In section 1 we introduce the …
On covers and envelopes in some functor categories
L Mao - Communications in Algebra, 2013 - Taylor & Francis
We study the existence of covers and envelopes by some special functors on the category of
finitely presented modules. As an application, we characterize some important rings using …
finitely presented modules. As an application, we characterize some important rings using …
Coherent rings and homologically finite subcategories
SA Sikko, SO Smalø - Mathematica Scandinavica, 1995 - JSTOR
For an arbitrary ring R (always associative with 1) we denote by Mod R th category of all left
R-modules and by mod R the full subcategory of Mod R wi objects the finitely presented …
R-modules and by mod R the full subcategory of Mod R wi objects the finitely presented …