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A set of all the operations on set $A$ is called an algebraic structure on set $A$?

Can anybody explain this statement to me.

What I understand from this is that, consider a set $\mathbb{N} $ then,

Algebraic structure on set $\mathbb{N}$ is the collection of all operators on $\mathbb{N}$ meaning,

Algebraic Structure $= \{+, \times, \cdots \} $?

I watched a couple of videos on YouTube about algebraic structure. Some of them seem to give some other different definitions of Algebraic Structures.

Can anyone explain what does it "precisely" refer to? The operator? Set of operators? The set $A$ itself?

William
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    This has been answered here already. For some links, see here. – Dietrich Burde Aug 20 '18 at 13:29
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    @DietrichBurde idk it's about why algebraic structures are used. My question is what exactly are Algebraic Structures? – William Aug 20 '18 at 13:37
  • This is also answered there. In particular, it says "a class of algebraic structures is called a variety of algebras if it can be defined using only equations (like $x\cdot (y\cdot z) = (x\cdot y) \cdot z$). Examples of varieties are groups, rings, modules, boolean algebras... Varieties are the core topic of study in the field of universal algebra". Did you have a look at other related links there? – Dietrich Burde Aug 20 '18 at 13:41
  • So one possible answer to your question (see title) "What do we refer to when we say algebraic structure?" is varieties of algebras. – Dietrich Burde Aug 20 '18 at 13:44

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