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As a computer science graduate who had only a basic course in abstract algebra, I want to study some abstract algebra in my free time. I've been looking through some books on the topic, and most seem to 'only' cover groups, rings and fields. Why is this the case? It seems to me you'd want to study simpler structures like semigroups, too. Especially looking at Wikipedia, there seems to be a huge zoo of different kinds of semigroups.

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    Well, the thing is, semigroups are *not* simpler that groups!2011-01-06
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    I am also a computer science graduate. (Although I am now determined to convert to mathematics.) It is true that semigroups are important to computer science. But I think the structures groups/rings/fields are of more importance to mathematicians. Also, if one understands the way of thinking behind these structures, it would not difficult for he or she to understand other structures, such as semigroups. For anyone, majored in computer science or mathematics or any other, abstract algebra tells people to think in the way of "structures". It is the way of thinking that is most benificial.2012-02-13

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