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# Algebraic structure

## Definition of the noun Algebraic structure

What does Algebraic structure mean as a name of something?

noun

1. [algebra] One or more sets together with a set of operations such that the sets are closed under the operations and are satisfying some axioms.

## Explanation

Algebraic structure: In mathematics, and more specifically in abstract algebra, the term algebraic structure generally refers to a set with one or more finitary operations defined on it.

• also known as 代数结构

## Printed dictionaries and other books with definitions for Algebraic structure

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### Secondary Calculus and Cohomological Physics (1998)

Proceedings of a Conference on Secondary Calculus and Cohomological Physics, August 24-31, 1997, Moscow, Russia by Marc Henneaux, Iosif Semenovich Krasilʹshchik, Aleksandr Mikhaĭlovich Vinogradov

Such an algebraic structure is a common feature of all supersymmetric ...

### Fundamentals of Computation Theory

12th International Symposium, FCT'99 Iasi, Romania, August 30 - September 3, 1999 Proceedings by Gabriel Ciobanu, Gheorghe Paun

the relevant algebraic structure is that of commutative monoids: the markings of the net can be regarded as elements of the free commutative monoid S⊕, and the structured transition system associated with N, denoted TS( N), ...

### Logic and Scientific Methods (1997)

Volume One of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence, August 1995 by Maria Luisa Dalla Chiara

Partial al9ebraic structures A partial algebraic structure is a set together with a collection of partial operations. A variety of algebraic structures of a given signature axiomatized by identities T (call the variety also T) gives rise to an associated ...

### Goal-Directed Proof Theory (2000)

by Dov M. Gabbay, N. Olivetti

semantics the algebraic structure is a semilattice. The semantics by Urquhart can be interestingly seen as a sort of metalevel codification of the bookkeeping mechanism used to control natural deduction proofs in relevant logics [Anderson and ...

### The VNR Concise Encyclopedia of Mathematics (2012)

by W. Gellert

An algebraic structure is a set on which certain operations (addition, multiplication, intersection etc.) are defined, where the exact nature of the objects of the set is irrelevant to the investigation. This concept of structure, which was developed at ...

### Abstract Algebra (2011)

Applications to Galois Theory, Algebraic Geometry and Cryptography by Celine Carstensen, Benjamin Fine, Gerhard Rosenberger

Briefly, an algebraic structure is a set S together with one or more binary operations on it satisfying axioms governing the operations. There are many algebraic structures but the most commonly studied structures are groups, rings, fields and ...

### Spectral Interpretation of Decision Diagrams (2006)

by Radomir Stankovic, Jaakko T. Astola

Thus, an algebraic structure is an abstraction of joint features of several ...

### Algebraic Methods in Philosophical Logic (2001)

by J. Michael Dunn, Gary Hardegree

appropriate algebraic structure is a monoid (M, +,0), where (M, +) is a semi-group and 0 is a distinguished element satisfying (Id) x + 0 = 0 + jc = x (identity). Besides the tedium of keeping track of 0 and ( ), which as "null entities" are a bit hard to ...

### Algebra: Form and Function, 2nd Edition (2015)

Form and Function by William G. McCallum, Eric Connally, Deborah Hughes-Hallett

Paying attention to algebraic structure means looking inside an algebraic. Example1 A student's grade in a course depends on two test grades, t1 and t2, and a final exam grade, f. The average of the two tests counts for 60% of the grade, and ...

### Dictionary of Logic as Applied in the Study of Language (2013)

Concepts/Methods/Theories by W. Marciszewski

algebraic structure; (b) a formal theory of algebraic structures. Algebraic structures 1. Logic .

### The Concise Oxford Dictionary of Mathematics (2009)

by Christopher Clapham, James Nicholson, James R. Nicholson

algebraic structure The term used to describe an abstract concept defined as consisting of certain elements with operations satisfying given axioms.

### The Penguin Dictionary of Mathematics (2008)

Fourth edition by David Nelson

algebraic structure A *set equipped with one or more * algebraic operations, usually required to satisfy a system of *axioms. Examples are ...

### Encyclopedia of Computer Science and Technology (2002)

Volume 45 - Supplement 30 by Allen Kent, James G. Williams

the underlying algebraic structure of confidence levels is a trilattice. Our next example illustrates this framework. Example 7 [Probabilistic DDB (24.35 )].

### Dictionary of philosophical terms (1997)

algebraic structure s algebraische Struktur f (mat) algorithm s Algorithmus m (mat) < logarithm algorithmic information s algotithmische ...

### The Facts on File Dictionary of Mathematics (2009)

by John Daintith, Richard Rennie

system is called an algebraic structure. algebra, Boolean See Boolean algebra . algebraic structure A structure imposed on elements of a set by certain operations that act on or combine the elements. The ambiguous x • x • combination of the ...

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