It has been observed that the category of all regular rings, when viewed as a full subcategory of the category of all rings, is not an algebraic variety. However if a regular ring is viewed as a ring equipped with a unary operation q such that xxqx = x and 0000q= 0, then the category of all rings with this added structure is indeed a variety but it is not, in any natural way, a subcategory of the category of all rings. In this article regular rings are viewed in this way and the free commutative regular rings are constructed. They are derived from the universal commutative regular ring associated with certain polynomial rings.
展开▼
