f] into a quotient algebra by extending the

binary operation [] to these equivalence classes.

b] - 1) for a, b [member of] [0, [infinity]) defines a normed binary operation.

We have the following simple observations about normed binary operation.

Henceforth, we assume that the normed binary operation [?

Let us define a new

binary operation on Q as follows:

r] _ : Q x Q [right arrow] Q is a binary operation on Q, a [[right arrow].

Define the binary operation a&b = [(b [[right arrow].

Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be a complete multi-space with a double binary operation set O([?

is also a multi-ring space with a double binary operation set O([?

For the case of finite groups, since there is only one

binary operation "x" and |x[?

SNA-rings are non-associative structure on which are defined two binary operations one associative and other being non-associative and addition distributes over multiplication both from right and left.

binary operation * is non-associative)such that the distributive laws a * (b + c) = a * b + a * c and (a + b) * c = a * c + b * c for all a, b, c in R.