Finding a small 3-connected minor maintaining a fixed minor and a fixed element

COMBINATORICA ◽  
1987 ◽  
Vol 7 (3) ◽  
pp. 231-242 ◽  
Author(s):  
Robert E. Bixby ◽  
C. R. Coullard
Keyword(s):  
Fixed Element

Post-quantum digital signature schemes: setting a hidden group with two-dimensional cyclicity

2020 ◽  
Vol 4 ◽  
pp. 75-82
Author(s):  
D.Yu. Guryanov ◽  
◽  
D.N. Moldovyan ◽  
A. A. Moldovyan ◽  
Keyword(s):  
Associative Algebra ◽  
Digital Signature ◽  
Quantum Signature ◽  
Commutative Group ◽  
Two Dimensional ◽  
Signature Scheme ◽  
Signature Schemes ◽  
Fixed Element ◽  
Commutative Associative Algebra ◽  
Quantum Digital Signature

For the construction of post-quantum digital signature schemes that satisfy the strengthened criterion of resistance to quantum attacks, an algebraic carrier is proposed that allows one to define a hidden commutative group with two-dimensional cyclicity. Formulas are obtained that describe the set of elements that are permutable with a given fixed element. A post-quantum signature scheme based on the considered finite non-commutative associative algebra is described.

scholarly journals Characterizations of m-Normal Nearlattices in terms of Principal n-Ideals

2013 ◽  
Vol 38 ◽  
pp. 49-59
Author(s):  
MS Raihan
Keyword(s):  
Prime Ideal ◽  
Prime Ideals ◽  
Single Element ◽  
Finitely Generated ◽  
Fixed Element ◽  
Minimal Prime

A convex subnearlattice of a nearlattice S containing a fixed element n?S is called an n-ideal. The n-ideal generated by a single element is called a principal n-ideal. The set of finitely generated principal n-ideals is denoted by Pn(S), which is a nearlattice. A distributive nearlattice S with 0 is called m-normal if its every prime ideal contains at most m number of minimal prime ideals. In this paper, we include several characterizations of those Pn(S) which form m-normal nearlattices. We also show that Pn(S) is m-normal if and only if for any m+1 distinct minimal prime n-ideals Po,P1,…., Pm of S, Po ? … ? Pm = S. DOI: http://dx.doi.org/10.3329/rujs.v38i0.16548 Rajshahi University J. of Sci. 38, 49-59 (2010)

FIXED ELEMENTS OF NONINJECTIVE ENDOMORPHISMS OF POLYNOMIAL ALGEBRAS IN TWO VARIABLES

2016 ◽  
Vol 95 (2) ◽  
pp. 209-213
Author(s):  
YUEYUE LI ◽  
JIE-TAI YU
Keyword(s):  
Associative Algebra ◽  
Characteristic Zero ◽  
Polynomial Algebra ◽  
Free Associative Algebra ◽  
Polynomial Algebras ◽  
Fixed Element ◽  
The Given

Let $A_{2}$ be a free associative algebra or polynomial algebra of rank two over a field of characteristic zero. The main results of this paper are the classification of noninjective endomorphisms of $A_{2}$ and an algorithm to determine whether a given noninjective endomorphism of $A_{2}$ has a nontrivial fixed element for a polynomial algebra. The algorithm for a free associative algebra of rank two is valid whenever an element is given and the subalgebra generated by this element contains the image of the given noninjective endomorphism.

scholarly journals English grammatical collocations of the verb and the preposition for and their collocational equivalents in the Slovak language

2021 ◽  
Vol 5 (S1) ◽  
pp. 1183-1194
Author(s):  
Marianna Hudcovičová ◽  
Ľudmila Jančovičová ◽  
Božena Petrášová ◽  
Jerome Baghana
Keyword(s):  
Empirical Research ◽  
Structure Data ◽  
Prepositional Phrase ◽  
Fixed Element ◽  
Parallel Corpus ◽  
Contrastive Study ◽  
Slovak Language ◽  
National Corpus

This paper focuses on empirical research of grammatical collocations of the type: verb and preposition FOR. Subject to analysis were the verbal prepostional structures of the pattern 1: V+prepositional phrase in the function of the object and the pattern 2: V+ preposition+fixed element.  The study is based on comparisons of the English and Slovak sentences containing this specific verbal-prepositional structure. Data for contrastive study of English and Slovak languages are taken from the electronic corpus Slovak National Corpus, ie. English- Slovak Parallel Corpus. The aim of the study is to analyse, describe and classify only prepositional counterparts.

scholarly journals Finite Groups Which Admit An Automorphism With Few Orbits

1960 ◽  
Vol 12 ◽  
pp. 73-100 ◽  
Author(s):  
Daniel Gorenstein
Keyword(s):  
Abelian Group ◽  
Direct Product ◽  
Finite Groups ◽  
Study Groups ◽  
Quaternion Group ◽  
Fixed Integer ◽  
Fixed Element ◽  
Odd Order ◽  
Special Case

In the course of investigating the structure of finite groups which have a representation in the form ABA, for suitable subgroups A and B, we have been forced to study groups G which admit an automorphism ϕ such that every element of G lies in at least one of the orbits under ϕ of the elements g, gϕr(g), gϕrϕ(g)ϕ2r(g), gϕr(g)ϕr2r(g)ϕ3r(g), etc., where g is a fixed element of G and r is a fixed integer.In a previous paper on ABA-groups written jointly with I. N. Herstein (4), we have treated the special case r = 0 (in which case every element of G can be expressed in the form ϕi(gj)), and have shown that if the orders of ϕ and g are relatively prime, then G is either Abelian or the direct product of an Abelian group of odd order and the quaternion group of order 8.

scholarly journals On P. Hall's Generalisation of a Theorem of Frobenius

1962 ◽  
Vol 5 (3) ◽  
pp. 97-100 ◽  
Author(s):  
S. K. Sehgal
Keyword(s):  
Finite Group ◽  
Greatest Common Divisor ◽  
Number Of Solutions ◽  
Fixed Element ◽  
A Finite Group

1. It is a well known theorem due to Frobenius that the number of solutions of the equationXn = 1in a finite group G, is a multiple of the greatest common divisor (n, g) of n and the order g of G. Frobenius himself proved later that the number of solutions of the equationXn = awhere a is a fixed element of G, is a multiple of (n, ga), ga being the order of the centralizer Z(a) of ain G.

Generators of Un(V) Over a Quasi Semilocal Semihereditary Ring

1981 ◽  
Vol 33 (5) ◽  
pp. 1232-1244 ◽  
Author(s):  
Hiroyuki Ishibashi
Keyword(s):  
Commutative Ring ◽  
Maximal Ideal ◽  
Valuation Ring ◽  
Hermitian Form ◽  
Free Module ◽  
Fixed Element ◽  
Semihereditary Ring ◽  
Maximal Ideals ◽  
Sesquilinear Form

Let o be a quasi semilocal semihereditary ring, i.e., o is a commutative ring with 1 which has finitely many maximal ideals {Ai|i ∊ I} and the localization oAi at any maximal ideal Ai is a valuation ring. We assume 2 is a unit in o. Furthermore * denotes an involution on o with the property that there exists a unit θ in o such that θ* = –θ. V is an n-ary free module over o with f : V × V → o a λ-Hermitian form. Thus λ is a fixed element of o with λλ* = 1 and f is a sesquilinear form satisfying f(x, y)* = λf(y, x) for all x, y in V. Assume the form is nonsingular; that is, the mapping M → Hom (M, A) given by x → f( , x) is an isomorphism. In this paper we shall write f(x, y) = xy for x, y in V.

scholarly journals The structure of a special class of near-rings

1972 ◽  
Vol 13 (2) ◽  
pp. 141-146 ◽  
Author(s):  
Steve Ligh
Keyword(s):  
Special Class ◽  
Negative Answer ◽  
Boolean Ring ◽  
Fixed Element

It is well known that a Boolean ring is isomorphic to a subdirect sum of two-element fields. In [3] a near-ring (B, +, ·) is said to be Boolean if there exists a Boolean ring (B, +, Λ, 1) with identity such that · is defined in terms of +, Λ, and 1 and, for any b ∈ B, b · b = b. A Boolean near-ring B is called special if a · b = (a ν x) Λ b, where x is a fixed element of B. It was pointed out that a special Boolean near-ring is a ring if and only if x = 0. Furthermore, a special Boolean near-ring does not have a right identity unless x = 0. It is natural to ask then whether any Boolean near-ring (which is not a ring) can have a right identity. Also, how are the subdirect structures of a special Boolean near-ring compared to those of a Boolean ring. It is the purpose of this paper to give a negative answer to the first question and to show that the subdirect structures of a special Boolean near- ring are very ‘close’ to those of a Boolean ring. In fact, we will investigate a class of near-rings that include the special Boolean near-rings and the Boolean semi- rings as defined in [8].

scholarly journals Relative annihilators in semilattices

1973 ◽  
Vol 9 (2) ◽  
pp. 169-185 ◽  
Author(s):  
J.C. Varlet
Keyword(s):  
Lower Bound ◽  
Principal Ideal ◽  
The Other ◽  
Fixed Element ◽  
Other Hand ◽  
The One ◽  
Implicative Semilattices

An α-distributive (respectively α-implicative) semilattice S is a lower semilattice (with greatest lower bound denoted by juxtaposition) in which the annihilator 〈x, a〉, that is {y ∈ S: xy ≤ α}, is an ideal (respectively a principal ideal) for the fixed element α and any x of S. These semilattices appear as natural links between general and distributive semi-lattices on the one hand, and between pseudo-complemented and implicative semilattices on the other hand. Prime and dense elements, as well as maximal and prime filters, are essential. Mandelker's result, a lattice L is distributive if and only if 〈x, y〉 is an ideal for any x, y ∈ L is extended to semi-lattices.

scholarly journals Solution of a functional equation on compact groups using Fourier analysis

2015 ◽  
Vol 69 (2) ◽  
pp. 9
Author(s):  
Abdellatif Chahbi ◽  
Brahim Fadli ◽  
Samir Kabbaj
Keyword(s):  
Functional Equation ◽  
Fourier Transform ◽  
Fourier Analysis ◽  
Compact Group ◽  
Compact Groups ◽  
Continuous Solutions ◽  
Fixed Element ◽  
Continuous Automorphism

Let \(G\) be a compact group, let \(n \in N\setminus \{0,1\}\) be a fixed element and let \(\sigma\) be a continuous automorphism on \(G\) such that \(\sigma^n=I\). Using the non-abelian Fourier transform, we determine the non-zero continuous solutions \(f:G \to C\) of the functional equation \[ f(xy)+\sum_{k=1}^{n-1}f(\sigma^k(y)x)=nf(x)f(y),\ x,y \in G,\] in terms of unitary characters of \(G\).

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