What's everyone's favorite modern/abstract algebra book? By that I
mean a book on algebraic structures, including:
(From Wikipedia)
Algebraic structures
Magma
Set S with binary operation +
Semigroup
Associativity of +
Monoid
Existence of identity element for + in S
Group
Existence of inverse elements for + in S
Abelian group
Commutativity of +
Pseudo-ring
Associative binary operation ·
Distributivity of · over +
Ring
Existence of identity element for · in S
Commutative ring
Commutativity of ·
Field
Existence of inverse elements for · in S
.. and linear algebra too would be part of the tree.
Basically good, very clear, hopefully fun or brief .. both would be
hard to believe in! A book along the line of Linear Algebra Done
Right by Sheldon Axler.
Please do not ask why I would care about theory!
-- Owen
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