BL-ALMOST DISTRIBUTIVE LATTICES

2012 ◽  
Vol 05 (02) ◽  
pp. 1250022 ◽  
Author(s):  
G. C. Rao ◽  
Naveen Kumar Kakumanu
Keyword(s):  
Distributive Lattice ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Distributive Lattices ◽  
Necessary And Sufficient

The concept of BL-almost distributive lattice (BL-ADL) is introduced and necessary and sufficient conditions for an ADL to become a BL-ADL are derived. Different characterizations of a BL-ADL are obtained.

Properties of Stone almost distributive lattices

2015 ◽  
Vol 08 (01) ◽  
pp. 1550011
Author(s):  
G. C. Rao ◽  
Mihret Alamneh
Keyword(s):  
Distributive Lattice ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Distributive Lattices ◽  
Basic Facts ◽  
Necessary And Sufficient

In this paper, we study different properties of Stone almost distributive lattice (Stone ADL), prove basic facts on a Stone ADL and derive a necessary and sufficient conditions for an ADL L to be a Stone ADL.

TOPOLOGICAL CHARACTERIZATION OF DUALLY NORMAL ALMOST DISTRIBUTIVE LATTICES

2012 ◽  
Vol 05 (03) ◽  
pp. 1250043
Author(s):  
G. C. Rao ◽  
N. Rafi ◽  
Ravi Kumar Bandaru
Keyword(s):  
Distributive Lattice ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Distributive Lattices ◽  
Prime Ideals ◽  
Topological Characterization ◽  
Maximal Ideals ◽  
Necessary And Sufficient

A dually normal almost distributive lattice is characterized topologically in terms of its maximal ideals and prime ideals. Some necessary and sufficient conditions for the space of maximal ideals to be dually normal are obtained.

Characterization of BL-almost distributive lattices

2015 ◽  
Vol 08 (03) ◽  
pp. 1550041 ◽  
Author(s):  
G. C. Rao ◽  
Naveen Kumar Kakumanu
Keyword(s):  
Distributive Lattice ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Distributive Lattices ◽  
Necessary And Sufficient

Necessary and sufficient conditions for an Almost Distributive Lattice (ADL) to become a BL-ADL are derived. Different characterization of a BL-ADL are obtained. Relation between the operators on BL-ADL are derived. Wide choice of fundamental operations for a BL-ADL are derived.

scholarly journals Subdirect products of semirings

2001 ◽  
Vol 26 (9) ◽  
pp. 539-545
Author(s):  
P. Mukhopadhyay
Keyword(s):  
Distributive Lattice ◽  
Subdirect Product ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Subdirect Products ◽  
Necessary And Sufficient

Bandelt and Petrich (1982) proved that an inversive semiringSis a subdirect product of a distributive lattice and a ring if and only ifSsatisfies certain conditions. The aim of this paper is to obtain a generalized version of this result. The main purpose of this paper however, is to investigate, what new necessary and sufficient conditions need we impose on an inversive semiring, so that, in its aforesaid representation as a subdirect product, the “ring” involved can be gradually enriched to a “field.” Finally, we provide a construction of fullE-inversive semirings, which are subdirect products of a semilattice and a ring.

scholarly journals Ideals on neutrosophic extended triplet groups

2021 ◽  
Vol 7 (3) ◽  
pp. 4767-4777
Author(s):  
Xin Zhou ◽  
◽  
Xiao Long Xin ◽  
Keyword(s):  
Prime Ideal ◽  
Distributive Lattice ◽  
Topological Structure ◽  
Hausdorff Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Prime Ideals ◽  
Ideal Space ◽  
Necessary And Sufficient

<abstract><p>In this paper, we introduce the concept of (prime) ideals on neutrosophic extended triplet groups (NETGs) and investigate some related properties of them. Firstly, we give characterizations of ideals generated by some subsets, which lead to a construction of a NETG by endowing the set consisting of all ideals with a special multiplication. In addition, we show that the set consisting of all ideals is a distributive lattice. Finally, by introducing the topological structure on the set of all prime ideals on NETGs, we obtain the necessary and sufficient conditions for the prime ideal space to become a $ T_{1} $-space and a Hausdorff space. </p></abstract>

FREE TERNARY ALGEBRAS

2000 ◽  
Vol 10 (06) ◽  
pp. 739-749 ◽  
Author(s):  
RAYMOND BALBES
Keyword(s):  
Distributive Lattice ◽  
Sufficient Conditions ◽  
Free Generator ◽  
Necessary And Sufficient Conditions ◽  
Finitely Generated ◽  
Bounded Distributive Lattice ◽  
Ternary Algebra ◽  
Free Generators ◽  
Ternary Algebras ◽  
Necessary And Sufficient

A ternary algebra is a bounded distributive lattice with additonal operations e and ~ that satisfies (a+b)~=a~b~, a~~=a, e≤a+a~, e~= e and 0~=1. This article characterizes free ternary algebras by giving necessary and sufficient conditions on a set X of free generators of a ternary algebra L, so that X freely generates L. With this characterization, the free ternary algebra on one free generator is displayed. The poset of join irreducibles of finitely generated free ternary algebras is characterized. The uniqueness of the set of free generators and their pseudocomplements is also established.

PRIME IDEAL CHARACTERIZATION OF STONE ADLs

2010 ◽  
Vol 03 (02) ◽  
pp. 357-367 ◽  
Author(s):  
U. M. Swamy ◽  
S. Ramesh ◽  
Ch. Shanthi Sundar Raj
Keyword(s):  
Prime Ideal ◽  
Distributive Lattice ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

In this paper we obtain certain necessary and sufficient conditions for an almost distributive lattice to become a Stone almost distributive lattice in topological and algebraic terms.

scholarly journals On Regular Elements in an Incline

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
A. R. Meenakshi ◽  
S. Anbalagan
Keyword(s):  
Distributive Lattice ◽  
Regular Ring ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Inverses ◽  
Regular Elements ◽  
Idempotent Semirings ◽  
Necessary And Sufficient

Inclines are additively idempotent semirings in which products are less than (or) equal to either factor. Necessary and sufficient conditions for an element in an incline to be regular are obtained. It is proved that every regular incline is a distributive lattice. The existence of the Moore-Penrose inverse of an element in an incline with involution is discussed. Characterizations of the set of all generalized inverses are presented as a generalization and development of regular elements in a∗-regular ring.

scholarly journals Functions and equations in classes of distributive lattices with pseudocomplementation

1974 ◽  
Vol 19 (2) ◽  
pp. 191-203
Author(s):  
R. Beazer
Keyword(s):  
Special Class ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Distributive Lattices ◽  
Necessary And Sufficient

In (8), R. L. Goodstein gave necessary and sufficient conditions for the solvability of equations over distributive lattices with 0 and 1 together with an algorithm for computing a solution whenever one exists. In addition, the same problem was considered for a special class of equations over distributive lattices with pseudocomplementation. The validity of several of Goodstein's results for distributive lattices without 0 and 1 was pointed out by Rudeanu in (15) and (16).

scholarly journals The quest for strong dualities

1995 ◽  
Vol 58 (2) ◽  
pp. 248-280 ◽  
Author(s):  
David M. Clark ◽  
Brian A. Davey
Keyword(s):  
Sufficient Conditions ◽  
Strong Duality ◽  
Necessary And Sufficient Conditions ◽  
Distributive Lattices ◽  
Necessary And Sufficient ◽  
Congruence Distributive

AbstractWe give a revised and updated exposition of the theory of full dualities initiated by Clark, Davey, Krauss and Werner, introducing the (stronger) notion of a strong duality. All known full dualities turn out to be strong. A series of theorems which provide necessary and sufficient conditions for a strong duality to exist is proved. All full dualities in the literature can be obtained from these results and many new strong dualities can be derived. In particular, we show that within congruence distributive varieties every duality can be upgraded to a strong duality. Amongst the new strong dualities are the dualities of Davey, Priestley and Werner for the varieties of pseudocomplemented distributive lattices which are either strong as they stand or can easily be made strong by the addition of partial operations to the dual structures.

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