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Page 8509 of Mathematical Reviews Vol. , Issue 2004k [page]

2004 Mathematical Reviews  
Soc. (3) 13 (1963), 31-50; MR 26 #1387], where it was also shown that families of such minimal primes form zero-dimensional spaces when provided with the hull-kernel topology.  ...  Topology Proc. 26 (2001/02), no. 2, 709-720. cient condition for a prime ideal to be minimal among all primes containing a fixed ideal was given in [J. Kist, Proc. London Math.  ... 

Priestley's Duality from Stone's

Isidore Fleisher
2000 Advances in Applied Mathematics  
This is the socalled "hull kernel" topology (the closure being described is "kernel-hull").  ...  Every T 0 -space is partially ordered by P ≤ Q just when Q ∈ P (T 0 = anti-symmetry; for the hull-kernel topology this gives the inclusion order among the prime filters).  ... 
doi:10.1006/aama.2000.0684 fatcat:m42vidrgnjgu3okvh5txado5ay

Ideal spaces: An extension of structure spaces of rings [article]

Themba Dube, Amartya Goswami
2022 arXiv   pre-print
The ideal spaces introduced in this paper allows such a study and our theory includes (but not restricted to) prime, maximal, minimal prime, strongly irreducible, irreducible, completely irreducible, proper  ...  of non-trivial idempotent elements in the ring.  ...  In [15] (see also [18] ), Henriksen and Jerison studied the hull-kernel topology on minimal prime ideals of a commutative ring.  ... 
arXiv:2203.09586v1 fatcat:svxh7kiwsfhwhhiq2gj4wa2lvq

Page 1152 of Mathematical Reviews Vol. 26, Issue 6 [page]

1963 Mathematical Reviews  
the hull- kernel topology.  ...  An isotone, inclusive and idempotent map of a poset is the closure operator (i.e., a topology through closed elements) in the poset.  ... 

Page 4933 of Mathematical Reviews Vol. , Issue 81M [page]

1981 Mathematical Reviews  
The author explores several properties of the conjugate hull which show that it is an analogue for conjugate extensions of the translational hull for ideal extensions.  ...  The author gives necessary and sufficient conditions for determinacy of connected, disconnected and finite posets in the class of all posets and for determinacy of posets in the class of all posets with  ... 

Page 1146 of Mathematical Reviews Vol. 47, Issue 5 [page]

1974 Mathematical Reviews  
With appropriate restrictions on T, the set of minimal prime elements can be equipped with a hull-kernel topology; the author shows that this topology is completely regular and has a base of open-and-  ...  The set S(P) of all residuated maps on P can be made into a weak partial Baer*-semigroup, and P is isomorphic to the orthomodular poset of closed projections in S(P). the author (Comm. Math.  ... 

The injective hull and the ${scr C}{scr L}$-compactification of a continuous poset

Rudolf-E. Hoffmann
1985 Canadian Journal of Mathematics - Journal Canadien de Mathematiques  
In [28], a characterization of continuous posets in terms of adjunctions (between partially ordered sets) has been given.  ...  only if L has at most one element.)  ...  The ^JP-topology on a continuous poset P is the trace of the ^JP-topology of the injective hull L of P. Proof.  ... 
doi:10.4153/cjm-1985-045-3 fatcat:wjwmbe2flfh5bb5r37zoezhs4e

Pro-finite MV-spaces

Antonio Di Nola, Revaz Grigolia
2004 Discrete Mathematics  
In this work it is shown that every MV-space, i.e. the prime ideal space of an MV-algebra, is pro-ÿnite if and only if it is a completely normal dual Heyting space.  ...  Acknowledgements We express our gratitude to the referee for her/his suggestions to improve the readability of this paper.  ...  Spec ÿ(A)be the space of all prime ideals of the Belluce lattice ÿ(A), equipped with the hull-kernel topology.  ... 
doi:10.1016/j.disc.2003.12.015 fatcat:ynp2xsktlbfwpjjxoao75jhhju

Pro-finite MV-spaces

A DINOLA
2004 Discrete Mathematics  
In this work it is shown that every MV-space, i.e. the prime ideal space of an MV-algebra, is pro-ÿnite if and only if it is a completely normal dual Heyting space.  ...  Acknowledgements We express our gratitude to the referee for her/his suggestions to improve the readability of this paper.  ...  Spec ÿ(A)be the space of all prime ideals of the Belluce lattice ÿ(A), equipped with the hull-kernel topology.  ... 
doi:10.1016/s0012-365x(04)00108-6 fatcat:qkr53fpf5be4dcfg44cle2r5yu

Complete Congruences on Topologies and Down-set Lattices

Marcel Erné, Mai Gehrke, Aleš Pultr
2006 Applied Categorical Structures  
From the work of Simmons about nuclei in frames it follows that a topological space X is scattered if and only if each congruence on the frame of open sets is induced by a unique subspace A so that = {  ...  We prove a seemingly similar but substantially different result about quasidiscrete topologies (in which arbitrary intersections of open sets are open): each complete congruence on such a topology is induced  ...  To illustrate, in the case of a Boolean algebra A, the structure X = S(A) is the poset of all prime filters of A (ordered by inclusion), and A * is that poset equipped with Stone's hull-kernel topology  ... 
doi:10.1007/s10485-006-9054-3 fatcat:h53b4jcpfzc5deemwbyvtmlzby

The hull-kernel topology on residuated lattices [article]

Saeed Rasouli, Amin Dehghani
2018 arXiv   pre-print
The notion of hull-kernel topology on a collection of prime filters in a residuated lattice is introduced and investigated.  ...  It is observed that any collection of prime filters is a T_0 topological space under the hull-kernel and the dual hull-kernel topologies.  ...  In this work we study the hull-kernel topology on a collection of prime filters in a residuated lattice.  ... 
arXiv:1812.11510v1 fatcat:4rkc3oyodjhnfjcnqdjcu2asta

Open Set Lattices of Subspaces of Spectrum Spaces

Y.T. Nai, D. Zhao
2015 Demonstratio Mathematica  
elements of L; (iii) we define the pure elements, a generalization of the notion of pure ideals in a multiplicative lattice and prove that for certain types of multiplicative lattices, the sub-poset of  ...  The motivating result is the well known fact that the topology of the spectrum of a commutative ring R with identity is isomorphic to the lattice of all radical ideals of R.  ...  One fundamental result proved here is that for any nonempty set S of prime elements of a multiplicative lattice L, the open set lattice of the hull kernel topology of S is isomorphic to the poset of all  ... 
doi:10.1515/dema-2015-0044 fatcat:anokxdllzjgmhni25krytk7r4y

a-minimal prime ideals in almost distributive lattices

Ch. Santhi Sundar Raj, K. Ramanuja Rao, S. Nageswara Rao
2021 Journal of Nonlinear Science and its Applications  
The concept of a-minimal prime ideal of an ADL is introduced and its characterizations are established. The set of all a-minimal prime ideals of an ADL is topologized and resulting space is studied.  ...  Acknowledgment The authors thanks the editor and anonymous reviewers for their careful reading and useful comments that have resulted in a significant improvement of the manuscript.  ...  The name hull-kernel topology is justified by the reason being that for any U ⊆ H, U = h H (k(U)), where U is the closure of U with respect to the hull-kernel topology on H.  ... 
doi:10.22436/jnsa.014.04.03 fatcat:gflcv6w5nbcxfe7dbdpcktqnia

Page 3447 of Mathematical Reviews Vol. , Issue 97F [page]

1997 Mathematical Reviews  
Using the usual hull-kernel construction, the authors then define a spectrum func- tor from the category of observation frames to the category of Ty topological spaces which is right adjoint to the embedding  ...  The adequate analogous notion in the setting of observation frames is that of M-topological systems; they are in one-to-one correspondence with observation frames whose codomain is a power set lattice.  ... 

Page 2563 of Mathematical Reviews Vol. , Issue 84g [page]

1984 Mathematical Reviews  
It is mainly concerned with the space of minimal prime ideals when it carries the hull-kernel topology.  ...  The hull-kernel topology on the set It of minimal prime ideals of a 0-distributive lattice $ is obtained by taking the family {{M},: xES}, where {M}, denotes the set {MEM: x EM}, as the base for open sets  ... 
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