770 research outputs found

    A note on distributivity of the lattice of L-ideals of a ring

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    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

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    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

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    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

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    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

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    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

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    The reticulation of an algebra AA is a bounded distributive lattice L(A){\cal L}(A) whose prime spectrum of filters or ideals is homeomorphic to the prime spectrum of congruences of AA, endowed with the Stone topologies. We have obtained a construction for the reticulation of any algebra AA from a semi-degenerate congruence-modular variety C{\cal C} in the case when the commutator of AA, applied to compact congruences of AA, produces compact congruences, in particular when C{\cal C} has principal commutators; furthermore, it turns out that weaker conditions than the fact that AA belongs to a congruence-modular variety are sufficient for AA 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 C{\cal C} is that of transferring algebraic and topological properties between the variety of bounded distributive lattices and C{\cal C}, 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

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    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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