On injective hulls of $$S$$ S -posets

2014 ◽  
Vol 91 (1) ◽  
pp. 62-70 ◽  
Author(s):  
Xia Zhang ◽  
Valdis Laan
Keyword(s):  
Injective Hulls

scholarly journals INJECTIVE MODULES OVER DOWN-UP ALGEBRAS

2010 ◽  
Vol 52 (A) ◽  
pp. 53-59 ◽  
Author(s):  
PAULA A. A. B. CARVALHO ◽  
CHRISTIAN LOMP ◽  
DILEK PUSAT-YILMAZ
Keyword(s):  
Roots Of Unity ◽  
Finiteness Conditions ◽  
Simple Modules ◽  
Injective Modules ◽  
Injective Hulls

AbstractThe purpose of this paper is to study finiteness conditions on injective hulls of simple modules over Noetherian down-up algebras. We will show that the Noetherian down-up algebras A(α, β, γ) which are fully bounded are precisely those which are module-finite over a central subalgebra. We show that injective hulls of simple A(α, β, γ)-modules are locally Artinian provided the roots of X2 − αX − β are distinct roots of unity or both equal to 1.

Constructing pure injective hulls

1980 ◽  
Vol 45 (3) ◽  
pp. 544-548 ◽  
Author(s):  
Wilfrid Hodges
Keyword(s):  
Abelian Group ◽  
Homomorphic Image ◽  
Injective Hull ◽  
Pure Extension ◽  
The One ◽  
Injective Hulls

Let A be an abelian group and B a pure injective pure extension of A. Then there is a homomorphic image C of B over A which is a pure injective hull of A; C can be constructed by using Zorn's lemma to find a suitable congruence on B. In a paper [4] which greatly generalises this and related facts about pure injectives, Walter Taylor asks (Problem 1.5) whether one can find a “construction” of C which is more concrete than the one mentioned above; he asks also whether the points of C can be explicitly described. In this note I return the answer No.

scholarly journals Injective Hulls of Simple Modules over Differential Operator Rings

2015 ◽  
Vol 43 (10) ◽  
pp. 4221-4230 ◽  
Author(s):  
Paula A. A. B. Carvalho ◽  
Can Hatipoğlu ◽  
Christian Lomp
Keyword(s):  
Differential Operator ◽  
Simple Modules ◽  
Injective Hulls

scholarly journals Injective hulls of monars over inverse semigroups

2013 ◽  
Vol 378 ◽  
pp. 207-216
Author(s):  
Boris M. Schein
Keyword(s):  
Inverse Semigroups ◽  
Injective Hulls

Injective Hulls of Semilattices

1970 ◽  
Vol 13 (1) ◽  
pp. 115-118 ◽  
Author(s):  
G. Bruns ◽  
H. Lakser
Keyword(s):  
Upper Bound ◽  
Partially Ordered Set ◽  
Binary Operation ◽  
Ordered Set ◽  
Upper Bounds ◽  
Partial Ordering ◽  
Partially Ordered ◽  
Image Position ◽  
Injective Hulls

A (meet-) semilattice is an algebra with one binary operation ∧, which is associative, commutative and idempotent. Throughout this paper we are working in the category of semilattices. All categorical or general algebraic notions are to be understood in this category. In every semilattice S the relationdefines a partial ordering of S. The symbol "∨" denotes least upper bounds under this partial ordering. If it is not clear from the context in which partially ordered set a least upper bound is taken, we add this set as an index to the symbol; for example, ∨AX denotes the least upper bound of X in the partially ordered set A.

Maximal (semi-)lattices of fractions and injective hulls

1995 ◽  
Vol 51 (1) ◽  
pp. 105-115
Author(s):  
W. Thurnherr ◽  
J. Schmid
Keyword(s):  
Injective Hulls
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