A bona fide scalar is a 1D semi-module over itself. More...

Concept definition

template<typename S>

concept dedekind::algebra::IsScalar = IsSemimodule<S, S>

dedekind::algebra::IsScalar

A bona fide scalar is a 1D semi-module over itself.

Definition modules.cppm:110

dedekind::algebra::IsSemimodule

A commutative additive monoid participating in a Linear Action: dedekind::category::IsSemimodule,...

Detailed Description

A bona fide scalar is a 1D semi-module over itself.

The scalar carrier S acts on itself by its own multiplication, forming the canonical 1D semi-module S over S. This is the minimal structural claim a type earns by being called a "scalar": it participates in its own linear action.

The field-level strengthening IsFieldElement<F> = IsVectorSpace<F, F> lives in algebra:vectorspace, alongside IsVectorSpace itself.