Rings whose kernel functors are linearly ordered
Rings whose kernel functors are linearly ordered are introduced here as a new non-commutative analogue of valuation rings: they include previous generalizations and coincide with them when commutativity is assumed. Unlike other generalized valuation rings, the defining property transfers nicely to matrix rings, thus enabling us to treat questions in a broader context. A semigroup structure imposed on the lattice of kernel functors is analyzed and the article concludes by examining when that semigroup can be thought of as the semigroup of a valuation ring. In addition, several examples are discussed throughout.
scientific article; zbMATH DE number 3957362
scientific article