scholarly journals Mutually algebraic structures and expansions by predicates

2013 ◽  
Vol 78 (1) ◽  
pp. 185-194 ◽  
Author(s):  
Michael C. Laskowski
Keyword(s):  
Algebraic Structure ◽  
Structure Theorem ◽  
Algebraic Structures ◽  
Finite Cover ◽  
Unary Predicate

AbstractWe introduce the notions of a mutually algebraic structures and theories and prove many equivalents. A theory T is mutually algebraic if and only if it is weakly minimal and trivial if and only if no model M of T has an expansion (M, A) by a unary predicate with the finite cover property. We show that every structure has a maximal mutually algebraic reduct. and give a strong structure theorem for the class of elementary extensions of a fixed mutually algebraic structure.

On single valued neutrosophic sets and neutrosophic א-structures: Applications on algebraic structures (hyperstructures)

2020 ◽  
pp. 108-117
Author(s):  
Madeleine Al Al-Tahan ◽  
◽  
◽  
Bijan Davvaz
Keyword(s):  
Algebraic Structure ◽  
Algebraic Structures ◽  
Neutrosophic Sets

In this paper, we find a relationship between SVNS and neutrosophic N-structures and study it. Moreover, we apply our results to algebraic structures (hyperstructures) and prove that the results on neutrosophic N-substructure (subhyperstructure) of a given algebraic structure (hyperstructure) can be deduced from single valued neutrosophic algebraic structure (hyperstructure) and vice versa.

An approach to fuzzy multi-ideals of near rings

2021 ◽  
pp. 1-11
Author(s):  
Madeline Al Tahan ◽  
Sarka Hoskova-Mayerova ◽  
Bijan Davvaz
Keyword(s):  
Algebraic Structure ◽  
Algebraic Structures

In recent years, fuzzy multisets have become a subject of great interest for researchers and have been widely applied to algebraic structures including groups, rings, and many other algebraic structures. In this paper, we introduce the algebraic structure of fuzzy multisets as fuzzy multi-subnear rings (multi-ideals) of near rings. In this regard, we define different operations on fuzzy multi-ideals of near rings and we generalize some results known for fuzzy ideals of near rings to fuzzy multi-ideals of near rings.

scholarly journals Logic and Truth: Some Logics without Theorems

2008 ◽  
pp. 104-117
Author(s):  
Jayanta Sen ◽  
Mihir Kumar Chakraborty
Keyword(s):  
Algebraic Structure ◽  
Logical Consequence ◽  
The Other ◽  
Algebraic Structures ◽  
Sequent Calculi

Two types of logical consequence are compared: one, with respect to matrix and designated elements and the other with respect to ordering in a suitable algebraic structure. Particular emphasis is laid on algebraic structures in which there is no top-element relative to the ordering. The significance of this special condition is discussed. Sequent calculi for a number of such structures are developed. As a consequence it is re-established that the notion of truth as such, not to speak of tautologies, is inessential in order to define validity of an argument.

Algebraic Structure of Step Traces and Interval Traces

2020 ◽  
Vol 175 (1-4) ◽  
pp. 253-280
Author(s):  
Ryszard Janicki ◽  
Łukasz Mikulski
Keyword(s):  
Algebraic Structure ◽  
Formal Analysis ◽  
Concurrent Systems ◽  
Interval Order ◽  
Canonical Forms ◽  
Algebraic Structures ◽  
Main Subject

Traces and their extensions as comtraces, step traces and interval traces are quotient monoids over sequences or step sequences that play an important role in the formal analysis and verification of concurrent systems. Step traces are generalizations of comtraces and classical traces while interval traces are specialized traces that can deal with interval order semantics. The algebraic structures and their properties as projections, hidings, canonical forms and other invariants are very well established for traces and fairly well established for comtraces. For step traces and interval traces they are the main subject of this paper.

Some Subfields of Qp, and their Non-Standard Analogues

1974 ◽  
Vol 26 (02) ◽  
pp. 473-491
Author(s):  
Diana L. Dubrovsky
Keyword(s):  
Algebraic Structure ◽  
Recursion Theory ◽  
Algebraic Structures ◽  
Mathematical Structures ◽  
Closed Fields ◽  
Standard Models ◽  
Algebraically Closed Fields

The desire to study constructive properties of given mathematical structures goes back many years; we can perhaps mention L. Kronecker and B. L. van der Waerden, two pioneers in this field. With the development of recursion theory it was possible to make precise the notion of "effectively carrying out" the operations in a given algebraic structure. Thus, A. Frölich and J. C. Shepherdson [7] and M. O . Rabin [13] studied computable algebraic structures, i.e. structures whose operations can be viewed as recursive number theoretic relations. A. Robinson [18] and E. W. Madison [11] used the concepts of computable and arithmetically definable structures in order to establish the existence of what can be called non-standard analogues (in a sense that will be specified later) of certain subfields of R and C, the standard models for the theories of real closed and algebraically closed fields respectively.

Stable theories with a new predicate

2001 ◽  
Vol 66 (3) ◽  
pp. 1127-1140 ◽  
Author(s):  
Enrique Casanovas ◽  
Martin Ziegler
Keyword(s):  
Group Structure ◽  
Finite Union ◽  
Small Subset ◽  
Finite Cover ◽  
Minimal Set ◽  
Unary Predicate ◽  
Elementary Substructure ◽  
Algebraic Set ◽  
Subspace Theorem ◽  
Image Position

Let M be an L-structure and A be an infinite subset of M. Two structures can be defined from A:• The induced structure on A has a name Rφ for every ∅-definable relation φ(M) ∩ An on A. Its language isA with its Lind-structure will be denoted by Aind.• The pair (M, A) is an L(P)-structure, where P is a unary predicate for A and L(P) = L ∪{P}.We call A small if there is a pair (N, B) elementarily equivalent to (M, A) and such that for every finite subset b of N every L–type over Bb is realized in N.A formula φ(x, y) has the finite cover property (f.c.p) in M if for all natural numbers k there is a set of φ–formulaswhich is k–consistent but not consistent in M. M has the f.c.p if some formula has the f.c.p in M. It is well known that unstable structures have the f.c.p. (see [6].) We will prove the following two theorems.Theorem A. Let A be a small subset of M. If M does not have the finite cover property then, for every λ ≥ ∣L∣, if both M andAindare λ–stable then (M, A) is λ–stable.Corollary 1.1 (Poizat [5]). If M does not have the finite cover property and N ≺ M is a small elementary substructure, then (M, N) is stable.Corollary 1.2 (Zilber [7]). If U is the group of wots of unity in the field ℂ of complex numbers the pair (ℂ, U) isω–stable.Proof. (See [4].) As a strongly minimal set ℂ is ω–stable and does not have the f.c.p. By the subspace theorem of Schmidt [3] every algebraic set intersects U in a finite union of translates of subgroups definable in the group structure of U alone. Whence Uind is nothing more than a (divisible) abelian group, which is ω–stable.

AN ALGEBRAIC STRUCTURE OF ZERO CURVATURE REPRESENTATIONS ASSOCIATED WITH COUPLED INTEGRABLE COUPLINGS AND APPLICATIONS TO τ-SYMMETRY ALGEBRAS

2011 ◽  
Vol 25 (23n24) ◽  
pp. 3237-3252 ◽  
Author(s):  
LIN LUO ◽  
WEN-XIU MA ◽  
ENGUI FAN
Keyword(s):  
Lie Algebras ◽  
Algebraic Structure ◽  
Algebraic Structures ◽  
Direct Sums ◽  
Zero Curvature ◽  
Integrable Couplings ◽  
Symmetry Algebras

We establish an algebraic structure for zero curvature representations of coupled integrable couplings. The adopted zero curvature representations are associated with Lie algebras possessing two sub-Lie algebras in form of semi-direct sums of Lie algebras. By applying the presented algebraic structures to the AKNS systems, we give an approach for generating τ-symmetry algebras of coupled integrable couplings.

Seeing Algebraic Structure: The Rubik's Cube

2020 ◽  
Vol 113 (5) ◽  
pp. 397-403
Author(s):  
Amanda Milewski ◽  
Daniel Frohardt
Keyword(s):  
High School ◽  
High School Students ◽  
Algebraic Structure ◽  
Algebraic Structures ◽  
School Students ◽  
Rubik's Cube ◽  
Rubik’S Cube

Few high school students associate mathematics with playfulness. In this paper, we offer a series of lessons focused on the underlying algebraic structures of the Rubik's Cube. The Rubik's Cube offers students an interesting space to enjoy the playful side of mathematics, while appreciating mathematics otherwise lost in routine experiences.

scholarly journals Involutory Quandles and Dichromatic Links

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 111
Author(s):  
Khaled Bataineh ◽  
Ilham Saidi
Keyword(s):  
Algebraic Structure ◽  
Algebraic Structures ◽  
Reidemeister Moves ◽  
Two Component

We define a new algebraic structure for two-component dichromatic links. This definition extends the notion of a kei (or involutory quandle) from regular links to dichromatic links. We call this structure a dikei that results from the generalized Reidemeister moves representing dichromatic isotopy. We give several examples on dikei and show that the set of colorings by these algebraic structures is an invariant of dichromatic links. As an application, we distinguish several pairs of dichromatic links that are symmetric as monochromatic links.

scholarly journals Bilinear Operators on Normed Linear Spaces

2019 ◽  
Vol 27 (1) ◽  
pp. 15-23
Author(s):  
Kazuhisa Nakasho
Keyword(s):  
Banach Space ◽  
Algebraic Structure ◽  
Algebraic Structures ◽  
Linear Spaces ◽  
The Third ◽  
Bilinear Operators ◽  
Normed Linear Spaces

Summary The main aim of this article is proving properties of bilinear operators on normed linear spaces formalized by means of Mizar [1]. In the first two chapters, algebraic structures [3] of bilinear operators on linear spaces are discussed. Especially, the space of bounded bilinear operators on normed linear spaces is developed here. In the third chapter, it is remarked that the algebraic structure of bounded bilinear operators to a certain Banach space also constitutes a Banach space. In the last chapter, the correspondence between the space of bilinear operators and the space of composition of linear opearators is shown. We referred to [4], [11], [2], [7] and [8] in this formalization.

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