Definition:Distributive Operation/Left
< Definition:Distributive Operation(Redirected from Definition:Left Distributive Operation)
Jump to navigation
Jump to search
Definition
Let $S$ be a set on which is defined two binary operations, defined on all the elements of $S \times S$, denoted here as $\circ$ and $*$.
The operation $\circ$ is left distributive over the operation $*$ if and only if:
- $\forall a, b, c \in S: a \circ \paren {b * c} = \paren {a \circ b} * \paren {a \circ c}$
Also see
Sources
- 1964: W.E. Deskins: Abstract Algebra ... (previous) ... (next): Exercise $1.4: \ 6$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 16$: The Natural Numbers: Exercise $16.23$
- 1970: B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra ... (previous) ... (next): Chapter $1$: Rings - Definitions and Examples: $1$: The definition of a ring: Definitions $1.1 \ \text{(c)}$