Stone Lattices. I: Construction Theorems

1969 ◽  
Vol 21 ◽  
pp. 884-894 ◽  
Author(s):  
C. C. Chen ◽  
G. Grätzer
Keyword(s):  
Representation Theory ◽  
Boolean Algebras ◽  
Prime Ideals ◽  
Satisfactory Theory

Stone lattices were (named and) first studied in 1957 (5). Since then, a great number of papers have been written on Stone lattices and a very satisfactory theory evolved. Despite the fact that all chains with 0, 1 as well as all Boolean algebras are Stone lattices, it turns out that many of the nice theorems on Boolean algebras have analogues, in fact, generalizations for Stone lattices. To give just two examples: the characterization of Boolean algebras in terms of prime ideals (Nachbin (6)) is generalized in (5) (see also (9)); Stone's representation theory (8) is generalized in (4); see also (2).

Characterization of prime ideals, filters in ABAs

2019 ◽  
Vol 13 (06) ◽  
pp. 2050106
Author(s):  
U. M. Swamy ◽  
R. Chudamani ◽  
K. Krishna Rao
Keyword(s):  
Boolean Algebras ◽  
Distributive Lattices ◽  
Prime Ideals ◽  
Equivalent Conditions

In this paper, we discuss several properties of ideals, filters, annihilators and maximisors in a general Almost Distributive Lattices (ADLs) and in particular, Almost Boolean Algebras (ABAs). Also, we characterize extreme ideals and filters. Further, several equivalent conditions are obtained in terms of ideals and filters for an ADL to become an ABA.

Common extension of Boolean informational systems

1979 ◽  
Vol 2 (1) ◽  
pp. 63-70
Author(s):  
Tadeusz Traczyk
Keyword(s):  
Information Systems ◽  
Boolean Algebras ◽  
Numerical Characterization ◽  
Common Extension

The notion of numerical characterization of Boolean algebras and coproducts are used to define information systems and to develop the theory of such systems.

scholarly journals On σ-complete prime ideals in Boolean algebras

1971 ◽  
Vol 22 (2) ◽  
pp. 209-214 ◽  
Author(s):  
Karel Prikry
Keyword(s):  
Boolean Algebras ◽  
Prime Ideals

scholarly journals Automorphisms of Regular Wreath Product -Groups

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Jeffrey M. Riedl
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Representation Theory ◽  
Wreath Product ◽  
Cyclic Group ◽  
Product Group ◽  
Finite Cyclic Group ◽  
Arbitrary Finite Group

We present a useful new characterization of the automorphisms of the regular wreath product group of a finite cyclic -group by a finite cyclic -group, for any prime , and we discuss an application. We also present a short new proof, based on representation theory, for determining the order of the automorphism group Aut(), where is the regular wreath product of a finite cyclic -group by an arbitrary finite -group.

On the Partially Ordered Set of Prime Ideals of a Distributive Lattice

1971 ◽  
Vol 23 (5) ◽  
pp. 866-874 ◽  
Author(s):  
Raymond Balbes
Keyword(s):  
Distributive Lattice ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Complete Characterization ◽  
Distributive Lattices ◽  
Prime Ideals ◽  
Partially Ordered ◽  
Irreducible Elements

For a distributive lattice L, let denote the poset of all prime ideals of L together with ∅ and L. This paper is concerned with the following type of problem. Given a class of distributive lattices, characterize all posets P for which for some . Such a poset P will be called representable over. For example, if is the class of all relatively complemented distributive lattices, then P is representable over if and only if P is a totally unordered poset with 0, 1 adjoined. One of our main results is a complete characterization of those posets P which are representable over the class of distributive lattices which are generated by their meet irreducible elements. The problem of determining which posets P are representable over the class of all distributive lattices appears to be very difficult.

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.

JAPAN’S EFFORTS TO DILUTE ITS DARK HISTORY THROUGH ANIME “HETALIA AXIS POWERS”

2018 ◽  
Vol 3 (2) ◽  
Author(s):  
Citra Rindu Prameswari
Keyword(s):  
World War Ii ◽  
Representation Theory ◽  
Image Representation ◽  
World War ◽  
Positive Image

“Hetalia” is one of many animes with history, specifically World War II, as its theme, but what makes it different from other animes is the fact that it gained many controversies even before it was broadcasted. The characters in “Hetalia” are world countries‟ personifications with stereotypes as their characteristics. Because of that, it can be seen easily that these characters automatically have ties with each respective country. Japan is Japan‟s character in it, but his scenes mainly only contain cultural related things rather than war-related activities. This article aims to find out the agenda behind Japan‟s image representation via “Hetalia’s” narrative plots and the characterization of Japan. Using cinema concept and representation theory to analyze the characterization through dialogues and narrations, I argue that there is a certain agenda to feminize to soften Japan‟s image and to dilute Japan‟s dark history so that Japan will have more positive image via “Hetalia”. It automatically highlights Japan‟s position as not one of the „main villains‟ in World War II by making one party look positively good (Japan) and another party look not so good in relation with geopolitics strategy.

Sign in / Sign up

Export Citation Format

Share Document