770 research outputs found
A note on distributivity of the lattice of L-ideals of a ring
Many studies have investigated the lattice of fuzzy substructures of algebraic structures such as groups and rings. In this study, we prove that the lattice of L-ideals of a ring is distributive if and only if the lattice of its ideals is distributive, for an infinitely ?- distributive lattice L. © 2019 Hacettepe University. All rights reserved
Smarandache near-rings
The main concern of this book is the study of Smarandache analogue properties of near-rings and Smarandache near-rings; so it does not promise to cover all concepts or the proofs of all results
Permutations of Massive Vacua
We discuss the permutation group G of massive vacua of four-dimensional gauge
theories with N=1 supersymmetry that arises upon tracing loops in the space of
couplings. We concentrate on superconformal N=4 and N=2 theories with N=1
supersymmetry preserving mass deformations. The permutation group G of massive
vacua is the Galois group of characteristic polynomials for the vacuum
expectation values of chiral observables. We provide various techniques to
effectively compute characteristic polynomials in given theories, and we deduce
the existence of varying symmetry breaking patterns of the duality group
depending on the gauge algebra and matter content of the theory. Our examples
give rise to interesting field extensions of spaces of modular forms.Comment: 44 pages, 1 figur
The pseudocomplementedness of modular lattices and its applications in groups
In this article, we first investigate pseudocomplemented inductive modular
lattices by using their a finite number of 0-sublattices. Then we use a finite
number of the 0-sublattices of a subgroup lattice to describe all locally
cyclic abelian groups. The results show us that a locally cyclic abelian group
can be characterized by its three number of subgroups.Comment:
Smarandache Near-rings
Generally, in any human field, a Smarandache Structure on a set A means a
weak structure W on A such that there exists a proper subset B contained in A
which is embedded with a stronger structure S.
These types of structures occur in our everyday's life, that's why we study
them in this book.
Thus, as a particular case:
A Near-ring is a non-empty set N together with two binary operations '+' and
'.' such that (N, +) is a group (not necessarily abelian), (N, .) is a
semigroup. For all a, b, c belonging to N we have (a + b) . c = a . c + b . c
A Near-field is a non-empty set P together with two binary operations '+' and
'.' such that (P, +) is a group (not-necessarily abelian), {P\{0}, .) is a
group. For all a, b, c belonging to P we have (a + b) . c = a . c + b . c
A Smarandache Near-ring is a near-ring N which has a proper subset P
contained in N, where P is a near-field (with respect to the same binary
operations on N).Comment: 200 pages, 50 tables, 20 figure
The Reticulation of a Universal Algebra
The reticulation of an algebra is a bounded distributive lattice whose prime spectrum of filters or ideals is homeomorphic to the prime
spectrum of congruences of , endowed with the Stone topologies. We have
obtained a construction for the reticulation of any algebra from a
semi-degenerate congruence-modular variety in the case when the
commutator of , applied to compact congruences of , produces compact
congruences, in particular when has principal commutators;
furthermore, it turns out that weaker conditions than the fact that belongs
to a congruence-modular variety are sufficient for to have a reticulation.
This construction generalizes the reticulation of a commutative unitary ring,
as well as that of a residuated lattice, which in turn generalizes the
reticulation of a BL-algebra and that of an MV-algebra. The purpose of
constructing the reticulation for the algebras from is that of
transferring algebraic and topological properties between the variety of
bounded distributive lattices and , and a reticulation functor is
particularily useful for this transfer. We have defined and studied a
reticulation functor for our construction of the reticulation in this context
of universal algebra.Comment: 29 page
The Lattices of Group Fuzzy Congruences and Normal Fuzzy Subsemigroups on E
The aim of this paper is to investigate the lattices of group fuzzy congruences and normal fuzzy subsemigroups on E-inversive semigroups. We prove that group fuzzy congruences and normal fuzzy subsemigroups determined each other in E-inversive semigroups. Moreover, we show that the set of group t-fuzzy congruences and the set of normal subsemigroups with tip t in a given E-inversive semigroup form two mutually isomorphic modular lattices for every t∈0,1
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