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Is an algebra or 'a algebra' the same thing as an algebraic structure? Or does it have a different meaning?


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Do you mean universal algebra? Or algebra over a field? It would really help if you mentioned, where (or in which context) you've encountered the term. – Martin Sleziak Jan 19 '13 at 7:26
BTW I fail to see why this question should be tagged elementary-set-theory. – Martin Sleziak Jan 19 '13 at 7:27
@Martin: Algebra is clearly a set... every question about sets is set theory, no? :-) – Asaf Karagila Jan 19 '13 at 8:40
x is a collection of number, with ring operation – Scott Jan 19 '13 at 11:01

Depends a bit on the context, but "an algebra" is often taken to mean a specific kind of algebraic structure, namely, a vector space with a multiplication operation (or a ring with a vector space structure). See, for example, this Wikipedia entry.

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