| ON STRONGLY REGULAR RINGS |
| |
| 作者姓名： | Huang Junmin |
| |
| 摘 要： | TheVonNeumannregularringsaredis-cussedinRef-lj.Weherediscussstronglyreg-ularringsbytheideaofsemigroupandcanob-tainsomenewresults.Definition1lJRingRiscalledstronglyregularring,ifitsatisfiesoneofthefollowingequivalentconditions:(1)Risaregularring,andeveryidempotentelementisacenterelement.(2)ForeveryaeR,thereexistsxsuchthata=a2x.(3)RisaregularringandRisreduced.Definition2L2]Cliffordsemigroupisareg-ularsemigroup,anditsidempotentisacenterel-ement.Hencewehavethefollowingtheorem:Theorem1IfSi…
|
ON STRONGLY REGULAR RINGS |
| |
| Huang Junmin.ON STRONGLY REGULAR RINGS[J].Journal of Shanghai Jiaotong university,1996(2). |
| |
| Authors: | Huang Junmin |
| |
| Institution: | Dept. of Applied Mathematics |
| |
| Abstract: | ?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. |
| |
| Keywords: | strongly regular ring maximum condition minimal condition idempotent element well-ordered chain |
| 本文献已被 CNKI 等数据库收录！ |
