Let
be a set of elements containing the unity
Definition
a, except condition
: Addition is commutative. Prove that condition
also hold.
Definition
a
Definition of a Ring
Suppose
is a set in which a relation of equality, denoted by
and
is a ring (with respect to these operations) if the following conditions are satisfied:
is closed under addition:
imply
Addition in
is associative:
:
Addition in
is closed under multiplication:
Multiplication in
is associative:
in
Two distributive laws hold in
:
in
The notation
will be used interchageably with
multiplication.
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Elements Of Modern Algebra
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- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,