A ring (R, +, *) is defined by a set R and two

binary operations (additive and multiplicative), so that:

(ii) A Hom-Maltsev algebra is a Hom-algebra (A, *, [alpha]) such that the

binary operation "*" is anticommutative and that the Hom-Maltsev identity

Let ([Q.sub.t],[*.sub.1]) and ([Q'.sub.t],[*.sub.2]) be two quantales, where [Q.sub.t] and are depicted in Figures 1 and 2 and the

binary operations [*.sub.1] and [*.sub.2] on both the quantales are the same as the meet operation in the lattices [Q.sub.t] and [Q'.sub.t] as shown in Tables 1 and 2.

We turn [Q.sub.k]/[Ker.sup.[].sub.f] into a quotient algebra by extending the

binary operation [] to these equivalence classes.

Henceforth, we assume that the normed

binary operation [??] on [0, [infinity]) x [0, [infinity]) satisfy the following properties:

is a well-defined

binary operation on the set of left cosets of H.

A non-empty set M is said to be a l-module over a ring R, if it is equipped with

binary operation +, s.m, [disjunction] and [conjunction] defined on it and satisfy the following conditions

From Definition 7 it follows that the

binary operation x is commutative and there exists the [mapping.sup.-1] : Q [right arrow] Q such that [x.sup.-1] x (x x y) = y holds.

By defining the new

binary operation on an AG-groupoid gives a semigroup, let (S, .) be an AG-groupoid, in [6], the operation "o" is defined as for x and y there exist a in S such that x o y = (xa)y, x,y [member of] S.

This note shows how to obtain an abelian group with an addition like operation (Joyner 2002:70-72) beginning with a subtraction

binary operation.

For example, consider the class of structures involving an ordering and a

binary operation (e.g.