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CLASSIFYING THICK SUBCATEGORIES OF PERFECT COMPLEXES
, 2006
"... Given a commutative coherent ring R, a bijective correspondence between the thick subcategories of perfect complexes Dper(R) and the Serre subcategories of finitely presented modules is established. To construct this correspondence, properties of the Ziegler and Zariski topologies on the set of (i ..."
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of (isoclasses for) indecomposable injective modules are essentially used.
MULTIPLICITIES OF INDECOMPOSABLE INJECTIVES
, 2004
"... Several results about the multiplicities of indecomposable injectives in the minimal injective resolution of a ring exist in the literature. Mostly these apply to universal enveloping algebras of finite dimensional solvable Lie algebras, and to Gorenstein noetherian PI local rings. We unify these ..."
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Several results about the multiplicities of indecomposable injectives in the minimal injective resolution of a ring exist in the literature. Mostly these apply to universal enveloping algebras of finite dimensional solvable Lie algebras, and to Gorenstein noetherian PI local rings. We unify
On categories of indecomposable modules. I
 OSAKA JOURNAL OF MATHEMATICS. 7(2) P.323P.344
, 1970
"... One of the authors had defined a regular additive category and studied some structures of it in [15]. We shall give, in this note, several applications of [15], Theorem 2. In the first section, we take an injective module M over a ring R and consider the full subcategory C(M) of the category of rig ..."
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Cited by 10 (0 self)
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One of the authors had defined a regular additive category and studied some structures of it in [15]. We shall give, in this note, several applications of [15], Theorem 2. In the first section, we take an injective module M over a ring R and consider the full subcategory C(M) of the category
THE STRUCTURE OF INDECOMPOSABLE INJECTIVES IN GENERIC REPRESENTATION THEORY
"... Abstract. This paper considers the structure of the injective objects IVn in the category F of functors between F2vector spaces. A coWeyl object Jλ is defined, for each simple functor Fλ in F. A functor is defined to be Jgood if it admits a finite filtration of which the quotients are coWeyl obj ..."
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Weyl objects. Properties of Jgood functors are considered and it is shown that the indecomposable injectives in F are Jgood. A finiteness result for proper subfunctors of coWeyl objects is proven, using the polynomial filtration of the shift functor ˜ ∆:F → F. This research is motivated by the Artinian
Deissler Rank Complexity of Powers of Indecomposable Injective Modules
, 1994
"... Abstract Minimality ranks in the style of Deissler are one way of measuring the structural complexity of minimal extensions of firstorder structures. In particular, positive Deissler rank measures the complexity of the injective envelope of a module as an extension of that module. In this paper we ..."
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Abstract Minimality ranks in the style of Deissler are one way of measuring the structural complexity of minimal extensions of firstorder structures. In particular, positive Deissler rank measures the complexity of the injective envelope of a module as an extension of that module. In this paper we
Explicit Description of a Class of Indecomposable Injective Modules*
"... Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p) 6 = 0. In this note, we describe the explicit structure of the injective envelope of the Rmodule R/p. ..."
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Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p) 6 = 0. In this note, we describe the explicit structure of the injective envelope of the Rmodule R/p.
ON THE STRUCTURE OF PRODUCED AND INIDUCED INDECOMPOSABLE LIE MODULES
"... l. Introd,ucti,on In recent years, it has become evident that certain indecomposable mod.ules are of basic importance to the representation theory of semisimple Lie algebras both over fields of characteristic 0 and over modular fields. If g is a semisimple Lie algebra and b a Borel subalgebra of g, ..."
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l. Introd,ucti,on In recent years, it has become evident that certain indecomposable mod.ules are of basic importance to the representation theory of semisimple Lie algebras both over fields of characteristic 0 and over modular fields. If g is a semisimple Lie algebra and b a Borel subalgebra of g
ONESIDED INDECOMPOSABLE PURE INJECTIVE MODULES OVER STRING ALGEBRAS
, 2004
"... We classify onesided indecomposable pure injective modules over (finite dimensional) string algebras. ..."
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We classify onesided indecomposable pure injective modules over (finite dimensional) string algebras.
INDECOMPOSABLE INJECTIVE MODULES OF FINITE MALCEV RANK OVER LOCAL COMMUTATIVE RINGS
, 2011
"... ..."
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