Let R be a primitive ring with nonzero socle, M a faithful irreducible right R-module, A the central-izer of M, and L= a direct sum of countably many minimal right ideals L, of R. Then there existsa family of subsetsi...Let R be a primitive ring with nonzero socle, M a faithful irreducible right R-module, A the central-izer of M, and L= a direct sum of countably many minimal right ideals L, of R. Then there existsa family of subsetsis infinite) of R such that L=R for any W, whereeach is a set of countably many orthogonal idempotent elements of rank one in R. Furthermore,there exists a primitive ring R and a direct sum L=of countably many minimal right ideals Li ofR, but R has no subset B =of countably many orthogonal idempotent elements of rank one such that and B can be extended to a corresponding basis of some basis of M over A.展开更多
?The multiplication semigroup of strongly regular ring R in the light of semigroup is researched,hence some properties of strongly regular rings are obtained. The non-division strongly regular ring R is anilpotent sem...?The multiplication semigroup of strongly regular ring R in the light of semigroup is researched,hence some properties of strongly regular rings are obtained. The non-division strongly regular ring R is anilpotent semisimple ring without identity element. It is neither the Artin ring nor the Noether ring. The setidempotents of ring R is an infinite set without the maximum and minimal conditions,it is a unions of someorder sets and hai a non-well-ordered order set at least.展开更多
Let R be a ring. We denote by · the so-called circle composition on R, defined by a(?)b=a+b-ab for a, b ∈R. Then (R, (?)) is a semigroup. We say that R is a generalized radical ring if (R, (?)) is a union of gr...Let R be a ring. We denote by · the so-called circle composition on R, defined by a(?)b=a+b-ab for a, b ∈R. Then (R, (?)) is a semigroup. We say that R is a generalized radical ring if (R, (?)) is a union of groups (a semigroup S is called展开更多
文摘Let R be a primitive ring with nonzero socle, M a faithful irreducible right R-module, A the central-izer of M, and L= a direct sum of countably many minimal right ideals L, of R. Then there existsa family of subsetsis infinite) of R such that L=R for any W, whereeach is a set of countably many orthogonal idempotent elements of rank one in R. Furthermore,there exists a primitive ring R and a direct sum L=of countably many minimal right ideals Li ofR, but R has no subset B =of countably many orthogonal idempotent elements of rank one such that and B can be extended to a corresponding basis of some basis of M over A.
文摘?The multiplication semigroup of strongly regular ring R in the light of semigroup is researched,hence some properties of strongly regular rings are obtained. The non-division strongly regular ring R is anilpotent semisimple ring without identity element. It is neither the Artin ring nor the Noether ring. The setidempotents of ring R is an infinite set without the maximum and minimal conditions,it is a unions of someorder sets and hai a non-well-ordered order set at least.
文摘Let R be a ring. We denote by · the so-called circle composition on R, defined by a(?)b=a+b-ab for a, b ∈R. Then (R, (?)) is a semigroup. We say that R is a generalized radical ring if (R, (?)) is a union of groups (a semigroup S is called
