scholarly journals Sheaf Representations and Duality in Logic

2021 ◽  
pp. 39-57
Author(s):  
Steve Awodey
Keyword(s):  
Sheaf Representations

scholarly journals A characterization of minimal prime ideals

1998 ◽  
Vol 40 (2) ◽  
pp. 223-236 ◽  
Author(s):  
Gary F. Birkenmeier ◽  
Jin Yong Kim ◽  
Jae Keol Park
Keyword(s):  
Positive Integer ◽  
Prime Ideal ◽  
Commutative Ring ◽  
Minimal Prime Ideal ◽  
Prime Ideals ◽  
Sheaf Representations ◽  
Minimal Prime

AbstractLet P be a prime ideal of a ring R, O(P) = {a ∊ R | aRs = 0, for some s ∊ R/P} | and Ō(P) = {x ∊ R | xn ∊ O(P), for some positive integer n}. Several authors have obtained sheaf representations of rings whose stalks are of the form R/O(P). Also in a commutative ring a minimal prime ideal has been characterized as a prime ideal P such that P= Ō(P). In this paper we derive various conditions which ensure that a prime ideal P = Ō(P). The property that P = Ō(P) is then used to obtain conditions which determine when R/O(P) has a unique minimal prime ideal. Various generalizations of O(P) and Ō(P) are considered. Examples are provided to illustrate and delimit our results.

MV-semirings and their Sheaf Representations

Order ◽  
2011 ◽  
Vol 30 (1) ◽  
pp. 165-179 ◽  
Author(s):  
Lawrence Peter Belluce ◽  
Antonio Di Nola ◽  
Anna Rita Ferraioli
Keyword(s):  
Sheaf Representations

scholarly journals Fully idempotent near-rings and sheaf representations

1998 ◽  
Vol 21 (1) ◽  
pp. 145-151
Author(s):  
Javed Ahsan ◽  
Gordon Mason
Keyword(s):  
Prime Ideals ◽  
Sheaf Representation ◽  
Strongly Regular ◽  
Sheaf Representations ◽  
Lattice Of Ideals

Fully idempotent near-rings are defined and characterized which yields information on the lattice of ideals of fully idempotent rings and near-rings. The space of prime ideals is topologized and a sheaf representation is given for a class of fully idempotent near-rings which includes strongly regular near-rings.

Sheaf representations of strongly harmonic rings

1985 ◽  
Vol 99 (3-4) ◽  
pp. 249-268 ◽  
Author(s):  
Harold Simmons
Keyword(s):  
Sheaf Representations

SynopsisWe describe five different sheaf representations of a ring, all of which are full and four of which are faithful. We give a characterization of strongly harmonic rings, and show that for such rings, the four faithful representations agree.

Sheaf representations of BL-algebras

2005 ◽  
Vol 9 (12) ◽  
pp. 897-909 ◽  
Author(s):  
L. Leuştean
Keyword(s):  
Sheaf Representations

scholarly journals Sheaf representations and locality of Riesz spaces with order unit

2021 ◽  
Vol 13 ◽  
Author(s):  
Antonio Di Nola ◽  
Giacomo Lenzi ◽  
Luca Spada
Keyword(s):  
Hausdorff Space ◽  
Spectral Space ◽  
Real Interval ◽  
Variety Of Algebras ◽  
Order Unit ◽  
Categorical Equivalence ◽  
Riesz Spaces ◽  
Algebraic Properties ◽  
Sheaf Representations ◽  
Strong Order

We present an algebraic study of Riesz spaces (=real vector lattices) with a (strong) order unit.  We exploit a categorical equivalence between those structures and a variety of algebras called RMV-algebras.  We prove two different sheaf representations for Riesz spaces with order unit: the first represents them as sheaves of linearly ordered Riesz spaces over a spectral space, the second represent them as sheaves of "local" Riesz spaces over a compact Hausdorff space.  Motivated by the latter representation we study the class of local RMV-algebras.  We study the algebraic properties of local RMV-algebra and provide a characterisation of them as special retracts of the real interval [0,1]. Finally, we prove that the category of local RMV-algebras is equivalent to the category of all Riesz spaces. 

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