Maximal essential extensions in the context of frames

2018 ◽  
Vol 79 (2) ◽  
Author(s):  
Richard N. Ball ◽  
Aleš Pultr
Keyword(s):  
Essential Extensions

scholarly journals On essential extensions of rings

1987 ◽  
Vol 35 (3) ◽  
pp. 379-386 ◽  
Author(s):  
E. R. Puczyłwski
Keyword(s):  
Ring Theory ◽  
Essential Ideal ◽  
Essential Extensions

This paper concerns the problem of description of the set of rings containing a given ring as an essential ideal. The results obtained are applied to some problems of ring theory and radicals.

scholarly journals Essential extensions of filters in residuated lattices

2021 ◽  
Author(s):  
Masoud Haveshki
Keyword(s):  
Boolean Algebra ◽  
Residuated Lattice ◽  
Residuated Lattices ◽  
Essential Extension ◽  
Mv Algebra ◽  
Essential Extensions

Abstract We define the essential extension of a filter in the residuated lattice A associated to an ideal of L(A) and investigate its related properties. We prove the residuated lattice A is a Boolean algebra, G(RL)-algebra or MV -algebra if and only if the essential extension of {1} associated to A \ P is a Boolean filter, G-filter or MV -filter (for all P ∈ SpecA), respectively. Also, some properties of lattice of essential extensions are studied.

On left ideal essential extensions of rings

2020 ◽  
Vol 162 (2) ◽  
pp. 539-548
Author(s):  
M. Nowakowska ◽  
E. R. Puczyłowski
Keyword(s):  
Left Ideal ◽  
Essential Extensions

scholarly journals ON MAXIMAL ESSENTIAL EXTENSIONS OF RINGS

2010 ◽  
Vol 83 (2) ◽  
pp. 329-337 ◽  
Author(s):  
R. R. ANDRUSZKIEWICZ
Keyword(s):  
Elementary Proof ◽  
Essential Extension ◽  
Essential Extensions

AbstractThe main purpose of this paper is to give a new, elementary proof of Flanigan’s theorem, which says that a given ring A has a maximal essential extension ME(A) if and only if the two-sided annihilator of A is zero. Moreover, we discuss the problem of description of ME(A) for a given right ideal A of a ring with an identity.

Essential extensions of Hausdorff spaces

1994 ◽  
Vol 2 (1) ◽  
pp. 101-105
Author(s):  
Horst Herrlich
Keyword(s):  
Hausdorff Spaces ◽  
Essential Extensions

scholarly journals Essentially closed radical classes

1983 ◽  
Vol 35 (1) ◽  
pp. 132-142 ◽  
Author(s):  
N. V. Loi
Keyword(s):  
The Other ◽  
Radical Class ◽  
Direct Sums ◽  
Ring Of Integers ◽  
Essential Extensions

AbstractThe main goal of this paper is to describe radical classes closed under essential extensions. It turns out that such classes are precisely the homomorphically closed semisimple classes, and hence a radical class is essentially closed if and only if it is subdirectly closed. Moreover, a class is closed under homomorphic images, direct sums and essential extensions if and only if it is an essentially closed radical class. Also radical classes are investigated which are closed under Dorroh essentially extensions only, such a radical class R consists of idempotent rings provided that R does not contain the ring of integers, meanwhile all the other radicals satisfy this requirement. A description of (hereditary and) Dorroh essentially closed radicals is given in Theorem 4.

scholarly journals The Zariski topology and essential extensions of semilattices

1990 ◽  
Vol 68 (1-2) ◽  
pp. 135-148
Author(s):  
Gerhard Gierz ◽  
Albert Stralka
Keyword(s):  
Zariski Topology ◽  
Essential Extensions

pg-Extensions and p-Extensions with applications to C(X)

2015 ◽  
Vol 14 (05) ◽  
pp. 1550068
Author(s):  
Papiya Bhattacharjee ◽  
Michelle L. Knox
Keyword(s):  
Commutative Rings ◽  
Essential Extension ◽  
Ring Extension ◽  
Principal Ideals ◽  
Contraction Map ◽  
Essential Extensions ◽  
Regular Rings

Essential extensions and p-extensions have been studied for commutative rings with identity in various papers, such as [P. Bhattacharjee, M. L. Knox and W. Wm. McGovern, p-Extensions, Proceedings for the OSU-Denison Conference, AMS series Contemporary Mathematics Series (to appear); p-Embeddings, Topology Appl. 160(13) (2013) 1566–1576; R. M. Raphael, Algebraic Extensions of Commutative Regular Rings, Canad. J. Math. 22(6) (1970) 1133–1155]. The present paper applies these concepts to certain subrings of C(X). Moreover, the paper introduces a new ring extension, called a pg-extension, and determines its relation to both essential extension and p-extension. It turns out that the pg-extension R ↪ S induces a well-defined contraction map between principal ideals [Formula: see text] and [Formula: see text].

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