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===소스=== | ===소스=== | ||
<references /> | <references /> | ||
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+ | ==메타데이터== | ||
+ | ===위키데이터=== | ||
+ | * ID : [https://www.wikidata.org/wiki/Q205464 Q205464] | ||
+ | ===Spacy 패턴 목록=== | ||
+ | * [{'LOWER': 'algebraic'}, {'LEMMA': 'structure'}] |
2021년 2월 17일 (수) 01:15 기준 최신판
노트
위키데이터
- ID : Q205464
말뭉치
- To study a non-algebraic object, it is often useful to use category theory to relate the object to an algebraic structure.[1]
- In full generality, an algebraic structure may use any number of sets and any number of axioms in its definition.[1]
- Loosely speaking, an algebraic structure is any set upon which "arithmetic-like operations have been defined.[2]
- Most of the important sets in Linear Algebra possess some type of algebraic structure, and abelian groups are the principal building block of virtually every one of these algebraic structures.[2]
- This is because the field axioms are extremely specific in describing algebraic structure.[2]
- A group is always a monoid, semigroup, and algebraic structure.[3]
- An algebraic structure may be based on other algebraic structures with operations and axioms involving several structures.[4]
- Every algebraic structure has its own notion of homomorphism, namely any function compatible with the operation(s) defining the structure.[4]
- In this way, every algebraic structure gives rise to a category.[4]
- Knowing the name ‘algebraic structure’ helps protect yourself from that.[5]
- Hence why they called the algebraic structure specification for JavaScript ‘Fantasy Land’.[5]
- A set with one or more binary operations gives rise to what is commonly known as an algebraic structure.[6]
- In particular, the set Z of integers under the addition ‘+’ is an algebraic structure.[6]
- In the same way, the set of rational numbers Q under the usual multiplication operation ‘x’, and denoted by (Q, x), is another algebraic structure.[6]
- Such an algebraic structure is denoted by (R, +, x).[6]
- An algebraic structure is a collection of objects and operations that can be used to calculate and solve equations.[7]
- A non-empty set G equipped with one or more binary operations is said to be an algebraic structure.[8]
- Suppose * is a binary operation on G. Then (G, *) is an algebraic structure.[8]
- By a property of an algebraic structure, we mean a property possessed by any of its operations.[8]
- There are several notions of an algebraic structure on an object of some category or higher category, which differ in generality.[9]
- We say that a functor in the base category preserves some algebraic structure if it lifts to the corresponding category of algebras.[9]
- In mathematics, and more specifically in abstract algebra, the term algebraic structure generally refers to an arbitrary set with one or more finitary operations defined on it.[10]
- For another example, the group can be seen as a set that is equipped with an algebraic structure, namely the operation .[10]
- We have a set, however to have algebraic structure we need one thing more.[11]
- For instance int set has operation of adding elements, then int set with adding operation - binary function int + int -> int , creates an algebraic structure, and in this example it is Semigroup.[11]
- Indeed, binary trees can represent expressions, and they form an algebraic structure.[12]
- The emphasis is on the algebraic nature of real automation, which appears as a natural three-sorted algebraic structure, that allows for a rich algebraic theory.[13]
소스
- ↑ 1.0 1.1 Outline of algebraic structures
- ↑ 2.0 2.1 2.2 13.2: Summary of Algebraic Structures
- ↑ Algebraic Structure - GeeksforGeeks
- ↑ 4.0 4.1 4.2 Algebraic structure
- ↑ 5.0 5.1 Algebraic Structures: Things I wish someone had explained about functional programming
- ↑ 6.0 6.1 6.2 6.3 Algebraic Structures,Group, Examples on Group
- ↑ Part C: Algebraic Structures (50 minutes)
- ↑ 8.0 8.1 8.2 Algebraic Structure and properties of structure | Discrete Mathematics
- ↑ 9.0 9.1 algebraic structure in nLab
- ↑ 10.0 10.1 What does algebraic structure mean?
- ↑ 11.0 11.1 Algebraic Structures Explained - Part 1 - Base Definitions
- ↑ Algebraic structure and programming
- ↑ Algebraic Structures in Automata and Database Theory
메타데이터
위키데이터
- ID : Q205464
Spacy 패턴 목록
- [{'LOWER': 'algebraic'}, {'LEMMA': 'structure'}]