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 , 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
Proper Fork algebras are algebras of binary relations extended with a binary operation
For example, consider the class of structures involving an ordering and a binary operation