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Someone have a good reference list for the classification of an algebrical structures? An example? Be: "a" for associative, "c" for commutative, "d" for distributive, "n" for neutro element, "o" for opposite/inverse, so, R(+,*) is d+acno*acno!0 and it's called "field". Tricky? "d" it's the last with parentesis for explain distributive related who, and if it's left or right, the simbols have the related property to their right! ("!0" mean not 0, it has not inverse about product in real)

Could someone prove a list of this type with relative name? Like before:

R(+,*): acno*acno!0 d(+, l, r) -> field

It will help me, because I remember the operation's property, but not the correct name.

Thank's previously and sorry for the bad Eglish(I'm Italian)

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    P.P.S. Your description of a field is still incomplete; it's missing the condition $1\neq 0$ (i.e., additive neutral element must be different from the multiplicative additive element). This also illustrates the difficulty in trying to come up with some sort of "simple" acronymic-style abbreviation for the desired properties.2012-02-01

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Not the symbolic solution you're looking for but a nice picture is available at https://mathoverflow.net/questions/72867/an-image-of-the-hierarchy-of-algebraic-structures:

enter image description here

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    Ne$a$t! It would be fu$n$ to play with the source of this, to expa$n$d it to include some of the missing links. For example, the jump from the rationals to reals and complexes puts in one tiny arrow almost the entirety of number theory. (And it looks like fields get commutativity added twice, skipping skew fields...)2012-02-01
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This page hosted by Peter Jipsen contains a list of 311 (as of today) named algebraic structures.

This wikipedia page also contains a lot of classification information on algebraic structures.

While neither of them has a simple table of the form you aspire from which to read off immediately the classification, you can presumably try to compile such a table yourself based on the information there. It may even be a worthwhile "cheatsheet" for future students of universal algebra.

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    It's what I'm thinking to do! A simple ordinated cheatsheet ;)2012-02-01