Injective Hulls in the Category of Mildly Distributive Semilattices

Order ◽  
2021 ◽  
Author(s):  
Changchun Xia
Keyword(s):  
Injective Hulls ◽  
Distributive Semilattices

scholarly journals O-Distributive Semilattices

1978 ◽  
Vol 21 (4) ◽  
pp. 469-475 ◽  
Author(s):  
Y. S. Pawar ◽  
And N. K. Thakare
Keyword(s):  
Sufficient Conditions ◽  
Distributive Semilattices

AbstractSufficient conditions for a semilattice to be a 0- distributive are obtained. Some equivalent formulations of 0- distributivity in a semilattice are given. Further, disjunctive 0- distributive semilattices are also characterized.

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.

scholarly journals Monotonic Distributive Semilattices

Order ◽  
2018 ◽  
Vol 36 (3) ◽  
pp. 463-486
Author(s):  
Sergio A. Celani ◽  
Ma. Paula Menchón
Keyword(s):  
Distributive Semilattices

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

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

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