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 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>

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 On cryptographic properties of (n + 1)-bit S-boxes constructed by known n-bit S-boxes

2020 ◽  
Vol 15 (1) ◽  
pp. 258-265
Author(s):  
Yu Zhou ◽  
Daoguang Mu ◽  
Xinfeng Dong
Keyword(s):  
Sufficient Conditions ◽  
Sum Of Squares ◽  
Basic Component ◽  
Necessary And Sufficient Conditions ◽  
Autocorrelation Functions ◽  
Walsh Spectrum ◽  
Cryptographic Algorithms ◽  
Necessary And Sufficient ◽  
Relationship Of

AbstractS-box is the basic component of symmetric cryptographic algorithms, and its cryptographic properties play a key role in security of the algorithms. In this paper we give the distributions of Walsh spectrum and the distributions of autocorrelation functions for (n + 1)-bit S-boxes in [12]. We obtain the nonlinearity of (n + 1)-bit S-boxes, and one necessary and sufficient conditions of (n + 1)-bit S-boxes satisfying m-order resilient. Meanwhile, we also give one characterization of (n + 1)-bit S-boxes satisfying t-order propagation criterion. Finally, we give one relationship of the sum-of-squares indicators between an n-bit S-box S0 and the (n + 1)-bit S-box S (which is constructed by S0).

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 Multigenerator Gabor Frames on Local Fields

2018 ◽  
Vol 33 (2) ◽  
pp. 307
Author(s):  
Owais Ahmad ◽  
Neyaz Ahmad Sheikh
Keyword(s):  
Sufficient Conditions ◽  
Complete Characterization ◽  
Necessary And Sufficient Conditions ◽  
Local Fields ◽  
Gabor Frames ◽  
Gabor System ◽  
Necessary And Sufficient

The main objective of this paper is to provide complete characterization of multigenerator Gabor frames on a periodic set $\Omega$ in $K$. In particular, we provide some necessary and sufficient conditions for the multigenerator Gabor system to be a frame for $L^2(\Omega)$. Furthermore, we establish the complete characterizations of multigenerator Parseval Gabor frames.

On the Ring of Quotients at a Prime Ideal of a Right Noetherian Ring

1972 ◽  
Vol 24 (4) ◽  
pp. 703-712 ◽  
Author(s):  
A. G. Heinicke
Keyword(s):  
Prime Ideal ◽  
Noetherian Ring ◽  
Quotient Ring ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Torsion Class ◽  
Ring Of Quotients ◽  
Ore Condition ◽  
The Right ◽  
Necessary And Sufficient

J. Lambek and G. Michler [3] have initiated the study of a ring of quotients RP associated with a two-sided prime ideal P in a right noetherian ring R. The ring RP is the quotient ring (in the sense of [1]) associated with the hereditary torsion class τ consisting of all right R-modules M for which HomR(M, ER(R/P)) = 0, where ER(X) is the injective hull of the R-module X.In the present paper, we shall study further the properties of the ring RP. The main results are Theorems 4.3 and 4.6. Theorem 4.3 gives necessary and sufficient conditions for the torsion class associated with P to have property (T), as well as some properties of RP when these conditions are indeed satisfied, while Theorem 4.6 gives necessary and sufficient conditions for R to satisfy the right Ore condition with respect to (P).

scholarly journals Cheap Talk and Editorial Control

2014 ◽  
Vol 14 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Jonathan Newton
Keyword(s):  
Information Transmission ◽  
Sufficient Conditions ◽  
Cheap Talk ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
Simple Models

AbstractThis paper analyzes simple models of editorial control. Starting from the framework developed by Krishna and Morgan (2001a), we analyze two-sender models of cheap talk where one or more of the senders has the power to veto messages before they reach the receiver. A characterization of the most informative equilibria of such models is given. It is shown that editorial control never aids communication and that for small biases in the senders’ preferences relative to those of the receiver, necessary and sufficient conditions for information transmission to be adversely affected are (i) that the senders have opposed preferences relative to the receiver and (ii) that both senders have powers of editorial control. It is shown that the addition of further senders beyond two weakly decreases information transmission when senders exercising editorial control are anonymous, and weakly increases information transmission when senders exercising editorial control are observed.

Stochastic Orders in Terms of Laplace Transforms

1995 ◽  
Vol 45 (3-4) ◽  
pp. 195-202 ◽  
Author(s):  
Asok K. Nanda
Keyword(s):  
Laplace Transform ◽  
Sufficient Conditions ◽  
Laplace Transforms ◽  
Necessary And Sufficient Conditions ◽  
Stochastic Orders ◽  
Partial Orderings ◽  
Life Distributions ◽  
Necessary And Sufficient

Recently s-FR and s-ST orderings have been defined in the literature. They are more general in the sense that most of the earlier known partial orderings reduce as particular cases of these orderings. Moreover, these orderings have helped in defining new and useful ageing criterion. In this paper, using Laplace transform, we characterize, by means of necessary and sufficient conditions. the property that two life distributions are ordered in the s-FR and s-ST sense. The characterization of LR, FR, MR, VR, STand HAMR orderings follow as particular cases.

scholarly journals A characterization of recurrent motions

1983 ◽  
Vol 28 (1) ◽  
pp. 1-4 ◽  
Author(s):  
Ronald A. Knight
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
Stable Flow

Necessary and sufficient conditions for a Poisson stable flow to be recurrent are given.

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