Definition:Opposite Ring

Definition

Let $\struct {R, +, \times}$ be a ring.

Let $* : R \times R \to R$ be the binary operation on $S$ defined by:

$\forall x, y \in S: x * y = y \times x$

The opposite ring of $R$ is the algebraic structure $\struct {R, +, *}$.

Also see

• Opposite Ring is Ring
• Opposite Ring of Opposite Ring
• Ring is Commutative iff Opposite Ring is Itself
• Definition:Ring Antihomomorphism

Sources

• 2003: P.M. Cohn: Basic Algebra: Groups, Rings and Fields ... (previous) ... (next): Chapter $4$: Rings and Modules: $\S 4.1$: The Definitions Recalled