A class of sub-almost distributive lattices in an associate almost distributive lattice through a filter

2019 ◽  
Vol 13 (07) ◽  
pp. 2050136
Author(s):  
S. Ramesh ◽  
Jogarao Gunda
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattice ◽  
Distributive Lattices ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Algebraic Properties ◽  
Necessary And Sufficient

In this paper, we introduce a class of sub-almost distributive lattices in an associate almost distributive lattice through a filter. We obtain several algebraic properties on the class of sub-almost distributive lattices and prove that the above class forms a distributive lattice. We derive a necessary and sufficient condition that the class to become a Boolean algebra.

Dense elements characterization of quasi-complemented Almost Distributive Lattices

2014 ◽  
Vol 07 (04) ◽  
pp. 1450062
Author(s):  
G. C. Rao ◽  
G. Nanaji Rao ◽  
A. Lakshmana
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattices ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The properties of the set D of dense elements of an ADL are studied. The filter congruence θD generated by D in quasi-complemented ADLs is characterized. Quasi-complemented ADLs is characterized in terms of dense elements. A necessary and sufficient condition for a quasi-complemented ADLs to become a Boolean algebra is established.

σ-Ideals in a 0-1 distributive lattice

2016 ◽  
Vol 09 (01) ◽  
pp. 1650025
Author(s):  
Y. S. Pawar ◽  
S. S. Khopade
Keyword(s):  
Distributive Lattice ◽  
Distributive Lattices ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complemented Lattices ◽  
Necessary And Sufficient

The notion of a [Formula: see text]-ideal in a [Formula: see text]-[Formula: see text] distributive lattice is introduced and studied. Certain classes of [Formula: see text]-[Formula: see text] distributive lattices such as normal lattices, complemented lattices, generalized Stone lattices are characterized by using the properties of [Formula: see text]-ideals. Stable ideals are defined and a necessary and sufficient condition for a [Formula: see text]-ideal to be stable is given.

KERNEL IDEALS IN ALMOST DISTRIBUTIVE LATTICES

2012 ◽  
Vol 05 (02) ◽  
pp. 1250024
Author(s):  
M. Sambasiva Rao ◽  
G. C. Rao
Keyword(s):  
Distributive Lattice ◽  
Distributive Lattices ◽  
Prime Ideals ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Kernel Ideal ◽  
Minimal Prime ◽  
Necessary And Sufficient ◽  
Equivalent Conditions

The concepts of ⋆-congruences and kernel ideals are introduced in a pseudo-complemented almost distributive lattice (ADL). A necessary and sufficient condition for a congruence to become a ⋆-congruence is derived. Some equivalent conditions for every ideal of a pseudo-complemented ADL to become a kernel ideal are derived. Prime kernel ideals are characterized in terms of minimal prime ideals. Properties of kernel ideals are observed in Stone ADLs.

scholarly journals Integral Cayley Multigraphs over Abelian and Hamiltonian Groups

10.37236/2742 ◽  
2013 ◽  
Vol 20 (2) ◽  
Author(s):  
Matt DeVos ◽  
Roi Krakovski ◽  
Bojan Mohar ◽  
Azhvan Sheikh Ahmady
Keyword(s):  
Boolean Algebra ◽  
Character Sums ◽  
Sufficient Condition ◽  
Normal Subgroups ◽  
Necessary And Sufficient Condition ◽  
Generating Set ◽  
Theoretic Proof ◽  
Necessary And Sufficient ◽  
Hamiltonian Groups ◽  
Integral Cone

It is shown that a Cayley multigraph over a group $G$ with generating multiset $S$ is integral (i.e., all of its eigenvalues are integers) if $S$ lies in the integral cone over the boolean algebra generated by the normal subgroups of $G$. The converse holds in the case when $G$ is abelian. This in particular gives an alternative, character theoretic proof of a theorem of Bridges and Mena (1982). We extend this result to provide a necessary and sufficient condition for a Cayley multigraph over a Hamiltonian group to be integral, in terms of character sums and the structure of the generating set.

Multi-Fuzzy Complex Nilpotent Matrices

2016 ◽  
Vol 5 (4) ◽  
pp. 52-76 ◽  
Author(s):  
Asit Dey ◽  
Madhumangal Pal
Keyword(s):  
Distributive Lattice ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complex Matrix ◽  
Fuzzy Matrix ◽  
Nilpotent Matrix ◽  
Nilpotent Matrices ◽  
Necessary And Sufficient

In this paper, the concept of multi-fuzzy matrix (MFM), multi-fuzzy complex matrix (MFCM), generalized multi-fuzzy complex matrix (GMFCM), generalized multi-fuzzy complex nilpotent matrix (GMFCNM) are introduced and have shown that the set of GMFCMs form a distributive lattice. Some properties and characterizations for GMFCNMs are established and in particular, a necessary and sufficient condition for an n × n GMFCNM to have the nilpotent index n is given. Finally, the reduction of GMFCNMs over a distributive lattice are given with some properties.

scholarly journals On annihilators in BL-algebras

2016 ◽  
Vol 14 (1) ◽  
pp. 324-337 ◽  
Author(s):  
Yu Xi Zou ◽  
Xiao Long Xin ◽  
Peng Fei He
Keyword(s):  
Boolean Algebra ◽  
Nonempty Subset ◽  
Sufficient Condition ◽  
Ideal Lattice ◽  
Necessary And Sufficient Condition ◽  
Finite Product ◽  
Brouwerian Lattice ◽  
Necessary And Sufficient ◽  
Complemented Lattice ◽  
The Ideal

AbstractIn the paper, we introduce the notion of annihilators in BL-algebras and investigate some related properties of them. We get that the ideal lattice (I(L), ⊆) is pseudo-complemented, and for any ideal I, its pseudo-complement is the annihilator I⊥ of I. Also, we define the An (L) to be the set of all annihilators of L, then we have that (An(L); ⋂,∧An(L),⊥,{0}, L) is a Boolean algebra. In addition, we introduce the annihilators of a nonempty subset X of L with respect to an ideal I and study some properties of them. As an application, we show that if I and J are ideals in a BL-algebra L, then $J_I^ \bot $ is the relative pseudo-complement of J with respect to I in the ideal lattice (I(L), ⊆). Moreover, we get some properties of the homomorphism image of annihilators, and also give the necessary and sufficient condition of the homomorphism image and the homomorphism pre-image of an annihilator to be an annihilator. Finally, we introduce the notion of α-ideal and give a notation E(I ). We show that (E(I(L)), ∧E, ∨E, E(0), E(L) is a pseudo-complemented lattice, a complete Brouwerian lattice and an algebraic lattice, when L is a BL-chain or a finite product of BL-chains.

scholarly journals A Note on Boolean Like Algebras

2018 ◽  
Vol 7 (4.10) ◽  
pp. 1015
Author(s):  
K. Pushpalatha ◽  
V. M.L.Hima Bindu
Keyword(s):  
Boolean Algebra ◽  
Sufficient Condition ◽  
Boolean Ring ◽  
Necessary And Sufficient Condition ◽  
Abstract System ◽  
Binary Operations ◽  
Necessary And Sufficient

In this paper we develop on abstract system: viz Boolean-like algebra and prove that every Boolean  algebra is a Boolean-like algebra.  A necessary and sufficient condition for a Boolean-like algebra to be a Boolean algebra has been obtained.  As in the case of Boolean ring  and Boolean algebra, it is established that under suitable binary operations the Boolean-like ring and Boolean-like algebra are equivalent abstract structures. 

scholarly journals A class of Lie racks associated to symmetric Leibniz algebras

2021 ◽  
pp. 2250230 ◽  
Author(s):  
Hamid Abchir ◽  
Fatima-ezzahrae Abid ◽  
Mohamed Boucetta
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Leibniz Algebras ◽  
Algebraic Properties ◽  
Necessary And Sufficient

We classify symmetric Leibniz algebras in dimensions 3 and 4 and we determine all associated Lie racks. Some of such Lie racks give rise to nontrivial topological quandles. We study some algebraic properties of these quandles and we give a necessary and sufficient condition for them to be quasi-trivial.

Multidimensional Iterative Interpolation

1991 ◽  
Vol 43 (2) ◽  
pp. 297-312 ◽  
Author(s):  
Gilles Deslauriers ◽  
Jacques Dubois ◽  
Serge Dubuc
Keyword(s):  
Euclidean Space ◽  
Discrete Subgroup ◽  
Interpolation Process ◽  
Sufficient Condition ◽  
Interpolation Function ◽  
Necessary And Sufficient Condition ◽  
Schwartz Distributions ◽  
Algebraic Properties ◽  
Iterative Interpolation ◽  
Necessary And Sufficient

AbstractWe define an iterative interpolation process for data spread over a closed discrete subgroup of the Euclidean space. We describe the main algebraic properties of this process. This interpolation process, under very weak assumptions, is always convergent in the sense of Schwartz distributions. We find also a convenient necessary and sufficient condition for continuity of each interpolation function of a given iterative interpolation process.

scholarly journals On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined Neutrosophic Linear Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Mohammad Abobala
Keyword(s):  
Linear Equations ◽  
Direct Application ◽  
Sufficient Condition ◽  
Algebraic Equations ◽  
Necessary And Sufficient Condition ◽  
Algebraic Properties ◽  
Invertible Elements ◽  
Necessary And Sufficient

This paper studies the problem of determining invertible elements (units) in any n-refined neutrosophic ring. It presents the necessary and sufficient condition for any n-refined neutrosophic element to be invertible, idempotent, and nilpotent. Also, this work introduces some of the elementary algebraic properties of n-refined neutrosophic matrices with a direct application in solving n-refined neutrosophic algebraic equations.

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