•A ring
R,
sometimes denoted by {R, +, x}, is a set of elements with two
binary operations, called addition and multiplication,
such that for all a, b, c in R the following axioms are obeyed.
•With
respect to addition
and multiplication,
the
set of all n-square
matrices over the real numbers is a ring.
•A
ring is said to be commutative if it
satisfies the following additional condition:
(M4)
Commutativity
of multiplication:
ab = ba for all a, b in R.
•Let S
be
the set of even integers (positive, negative, and 0) under the usual operations
of
addition and multiplication. S is a commutative ring.
•The set Zn of integers {0, 1, … , n
- 1},
together with the arithmetic operations modulo n, is a commutative ring
Rings - Examples
•The
set of all even
integers,
positive, negative, and zero, under the operations arithmetic addition and
multiplication.
•The set
of all
integers
under the operations of arithmetic addition and multiplication.
•The set
of all
real numbers
under the operations of arithmetic
addition
and multiplication.
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