It is shown that the set {1, 2, . . . , n} contains at most 2n/2−2n maximal sum-free subsets, provided n is large enough. A set A ⊆ [n] = {1, 2, . . . , n} is sum-free if for any two elements a, b ∈ A we have a + b / ∈ A. A sum-free set A ⊆ [n] is maximal if it is not contained in any other sum-free subset of [n]. Let s(n) and smax(n) denote the number of sum-free and maximal sum-free subsets o...

The rings considered in this article are commutative with identity $1neq 0$. By a proper ideal of a ring $R$,  we mean an ideal $I$ of $R$ such that $Ineq R$.  We say that a proper ideal $I$ of a ring $R$ is a  maximal non-prime ideal if $I$ is not a prime ideal of $R$ but any proper ideal $A$ of $R$ with $ Isubseteq A$ and $Ineq A$ is a prime ideal. That is, among all the proper ideals of $R$,...

A finite p-group is said to be of Gorenstein-Kulkarni type if the set of all elements of non-maximal order is a maximal subgroup. 2-groups of Gorenstein-Kulkarni type arise naturally in the study of group actions on compact Riemann surfaces. In this paper, we proceed towards a classification of p-groups of Gorenstein-Kulkarni type. Mathematics Subject Classification: 20D15, 20E15, 30F20.

A tope committee K for a simple oriented matroid M is a subset of its maximal covectors such that every positive halfspace of M contains more than a half of the maximal covectors from K. The structures of the family of all committees for M, and of the family of its committees that contain no pairs of opposites, are described. Farey subsequences associated to the elements of the mth layer of the...

MAXIMAL QUOTIENT RINGS AND ESSENTIAL RIGHT IDEALS IN GROUP RINGS OF LOCALLY FINITE GROUPS Theorem . zero . FERRAN CEDÓ * AND BRIAN HARTLEY Dedicated to the memory of Pere Menal Let k be a commutative field . Let G be a locally finite group without elements of order p in case char k = p > 0 . In this paper it is proved that the type I. part of the maximal right quotient ring of the group algebgr...

Several arguments have been proposed some years ago, attempting to prove the impossibility of defining Lorentz-invariant elements of reality. I find that a sufficient condition for the existence of elements of reality, introduced in these proofs, is in fact also used as a necessary condition. I argue that Lorentz-invariant elements of reality can be defined but, as Vaidman pointed out, they won...

There has been much work on strong and weak Lefschetz conditions for graded Artinian algebras A, especially those that are Gorenstein. A more general invariant of an algebra or finite A-module M we consider here is the set Jordan types elements maximal ideal

What ingredients are necessary to describe all maximal subgroups of the general finite group G? This paper is concerned with providing such an analysis. A good first reduction is to take into account the first isomorphism theorem, which tells us that the maximal subgroups containing a given normal subgroup N of G correspond, under the natural projection, to the maximal subgroups of the quotient...

in this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. some results about existence of maximal m-open setsare given. moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.our results are supported by examples and counterexamples.