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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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    Why would anyone want to complicate matters by adding an obscure abbreviation?2012-01-31
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    It's not an obscure abbreviation, it' more easy to remember because let only the keyword. Why mathemathics use R(+,\*) instead of: "The set named 'R' where there are defined two binary operators named repectively '+' and '\*'"? Because is easier!2012-01-31
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    Abbreviations of the type you suggest can be seen in some parts of mathematics, and even more frequently in theoretical computer science. So they are obviously viewed as useful by many pople.2012-01-31
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    Not that it is directly relevant, but a structure with two binary operations, $+$, and $*$, where each is associative, commutative, and has a neutral element, and in which $*$ distributes over $+$ (your notation does not seem to distinguish who distributes over who; this is important!) is not necessarily a field, it's not even necessarily a [semiring](http://en.wikipedia.org/wiki/Semiring)! You are missing additive inverses to get a commutative ring, and multiplicative inverses of nonzero elements to get a field.2012-01-31
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    I typed list like this, not equal, if you have a best proposal, please, I very need of it! For the field, I was wrong I know, I'll fix it speedly! :D2012-02-01
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    I have trouble understanding your request; you say you want a list in which the properties of the operations are described by a single word (which, so far, is related to its standard name); yet you say you want the list because you have trouble remembering the standard name of the properties and remember only what they are. If that is the case, it would seem that such a list would be confusing! You would need to: (i) look up the abbreviation, and then (ii) look up the definition. How is this better than looking up the definition? (cont)2012-02-01
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    (cont) Also, there are a *lot* of algebraic structures (magmas, moufang loops, quasigroups, semigroups, monoids, commutative monoids, and so on and so on) and not all of them can be defined in terms of properties of their operations in an equational manner (e.g., inverse semigroups). I can see offering a list of important and common structures, and letting *you* come up with whatever scheme you want to remember them, but to offer such a scheme here would, I think, qualify as "too localized". It wouldn't be of any help to anybody but you, *if* it were of any help to you at all.2012-02-01
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    For a slightly more in-depth discussion of the point @Arturo raised in his last comment, see [this wikipedia page](http://en.wikipedia.org/wiki/Algebraic_structure). If I understand correctly, Arturo is trying to draw your attention to the difference between the [first section](http://en.wikipedia.org/wiki/Algebraic_structure#Structures_whose_axioms_are_all_identities) of that page and [the second section](http://en.wikipedia.org/wiki/Algebraic_structure#Structures_with_some_axioms_that_are_not_identities).2012-02-01
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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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