K-algebra

-monoid

A -monoid is an K-algebra for which the bilinear product possesses a two-sided identity and is associative falg

• for all
• for all

Hence it is also called a unital associative algebra over . In other words, a -monoid is a field action on a ring. An algebra homomorphism which preserves the identity is a unital algebra homomorphism or -monoid homomorphism. A generalization is an R-monoid.

Further terminology

• Algebraic element

Examples

• Matrix algebra over a field
• Complex number
• Quaternion (non-commutative)
• Endomorphism ring
• Tensor algebra
• Clifford algebra
• Extension field as a unital associative algebra

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