scholarly journals Related representation theorems for rings, semi-rings, near-rings and semi-near-rings by partial transformations and partial endomorphisms

1977 ◽  
Vol 20 (4) ◽  
pp. 307-315 ◽  
Author(s):  
Hanns Joachim Weinert
Keyword(s):  
Commutative Group ◽  
Representation Theorems ◽  
Ring Of Endomorphisms ◽  
Associative Rings

Fundamental statements for (associative) rings are that (a) the endomorphisms of each commutative group (U, +) form a ring and (b) eachring may be embedded in such a ring of endomorphisms. In order to generalise these theorems to groups and rings whose addition may not be commutative, one has to deal with partial endomorphisms. But thesering-theoretical Theorems 4a and 4b turn out to be specialisations of similarones for semi-near-rings, near-rings and semirings, developed here inSection 2 after some preliminaries on semi-near-rings in Section 1. A glance at Definition 1 and the ring-theoretical theorems and remarks at the end of Section 2 may give more orientation.

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.

Representation Theorems for Terms in a Certain Model for Information Systems

1982 ◽  
Vol 5 (1) ◽  
pp. 1-14
Author(s):  
Bernd Reusch ◽  
Gerd Szwillus
Keyword(s):  
Information Systems ◽  
Normal Forms ◽  
Abstract Model ◽  
Representation Theorems

We study a term-language, which is used by the “Warsaw-School” in an abstract model for information systems. Various normal forms as well as standard expansions with respect to product terms are formulated and proved correct. It is shown that the shortest sums of so-called maximal sub-products are the shortest representations of terms and algorithms for their generation are given.

scholarly journals Signature-Based Representations for the Reliability of Systems with Heterogeneous Components

2011 ◽  
Vol 48 (03) ◽  
pp. 856-867 ◽  
Author(s):  
Jorge Navarro ◽  
Francisco J. Samaniego ◽  
N. Balakrishnan
Keyword(s):  
Coherent Systems ◽  
Representation Theorems ◽  
Performance Of Systems ◽  
Independent And Identically Distributed

Signature-based representations of the reliability functions of coherent systems with independent and identically distributed component lifetimes have proven very useful in studying the ageing characteristics of such systems and in comparing the performance of different systems under varied criteria. In this paper we consider extensions of these results to systems with heterogeneous components. New representation theorems are established for both the case of components with independent lifetimes and the case of component lifetimes under specific forms of dependence. These representations may be used to compare the performance of systems with homogeneous and heterogeneous components.

scholarly journals Density and representation theorems for multipliers of type (p, q)

1967 ◽  
Vol 7 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Alessandro Figà-Talamanca ◽  
G. I. Gaudry
Keyword(s):  
Linear Operator ◽  
Bounded Linear Operator ◽  
Important Class ◽  
Lebesgue Spaces ◽  
Representation Theorems ◽  
Locally Compact ◽  
Bounded Linear ◽  
Character Group ◽  
Hausdorff Group ◽  
Lca Group

Let G be a locally compact Abelian Hausdorff group (abbreviated LCA group); let X be its character group and dx, dx be the elements of the normalised Haar measures on G and X respectively. If 1 < p, q < ∞, and Lp(G) and Lq(G) are the usual Lebesgue spaces, of index p and q respectively, with respect to dx, a multiplier of type (p, q) is defined as a bounded linear operator T from Lp(G) to Lq(G) which commutes with translations, i.e. τxT = Tτx for all x ∈ G, where τxf(y) = f(x+y). The space of multipliers of type (p, q) will be denoted by Lqp. Already, much attention has been devoted to this important class of operators (see, for example, [3], [4], [7]).

Varieties satisfying semigroup identities: Algebras over a finite field and rings

2016 ◽  
Vol 26 (05) ◽  
pp. 985-1017
Author(s):  
Olga B. Finogenova
Keyword(s):  
Finite Field ◽  
Associative Algebras ◽  
Adjoint Semigroup ◽  
Semigroup Identities ◽  
Associative Rings

We study varieties of associative algebras over a finite field and varieties of associative rings satisfying semigroup or adjoint semigroup identities. We characterize these varieties in terms of “forbidden algebras” and discuss some corollaries of the characterizations.

Small Riesz spaces

1989 ◽  
Vol 105 (3) ◽  
pp. 523-536 ◽  
Author(s):  
G. Buskes ◽  
A. van Rooij
Keyword(s):  
Representation Theory ◽  
Direct Method ◽  
Riesz Space ◽  
Pictorial Representation ◽  
Representation Theorems ◽  
Riesz Spaces ◽  
Number Of Authors

Many facts in the theory of general Riesz spaces are easily verified by thinking in terms of spaces of functions. A proof via this insight is said to use representation theory. In recent years a growing number of authors has successfully been trying to bypass representation theorems, judging them to be extraneous. (See, for instance, [9,10].) In spite of the positive aspects of these efforts the following can be said. Firstly, avoiding representation theory does not always make the facts transparent. Reading the more cumbersome constructions and procedures inside the Riesz space itself one feels the need for a pictorial representation with functions, and one suspects the author himself of secret heretical thoughts. Secondly, the direct method leads to repeating constructions of the same nature over and over again.

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