An Ascending Chain Condition on Wedderburn Radicals |
| |
| Authors: | Nam Kyun Kim Sung Ju Ryu |
| |
| Affiliation: | 1. Division of General Education , Hanbat National University , Daejeon, Korea;2. Department of Mathematics Education , Pusan National University , Pusan, South Korea |
| |
| Abstract: | In this note we study the properties of Amitsur's example for Wedderburn radicals, introducing the concept of W n -reduced rings. The theories of commutative ring and reduced ring are generalized to W n -reduced rings. We characterize the W n -reduced property and study properties of W n -reduced rings. It is shown that the classes of semi-commutative rings, W n -reduced rings, and 2-primal rings are in a strictly increasing order. We extend the class of W n -reduced rings, observing various kinds of extensions containing classical quotient rings, polynomial rings, and power series rings. Communicated by M. Ferrero. |
| |
| Keywords: | Amitsur's example for Wedderburn radical Classical quotient ring Polynomial ring Wedderburn radical W n -reduced ring |
|
|
