Definition:Ring (Abstract Algebra)/Product

Definition

Let $\struct {R, *, \circ}$ be a ring.

The distributive operation $\circ$ in $\struct {R, *, \circ}$ is known as the ring product.

Also known as

The operation of ring product is also known as multiplication.

However, on $\mathsf{Pr} \infty \mathsf{fWiki}$ it is preferred that multiplication is kept to the conventional meaning as applied to multiplication of numbers.

Hence, in the context of the general ring, the word product is mandatory, except in specific cases (for example, the case of matrix multiplication) where the term multiplication is established.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $21$. Rings and Integral Domains
• 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 $1.1 \ \text{(c)}$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): ring
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): ring