# Definition:Ring (Abstract Algebra)/Product

< Definition:Ring (Abstract Algebra)(Redirected from Definition:Ring Product)

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## 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

Some sources call this **multiplication**, but on this website it is preferred that this word is kept to the conventional meaning as applied to multiplication of numbers.

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 $1.1 \ \text{(c)}$