Unit-Regularity of Regular Nilpotent Elements

作者：Khurana Dinesh^*

来源：Algebras and Representation Theory, 2016, 19(3): 641-644.

DOI：10.1007/s10468-015-9592-1

• Regular elements
• Nilpotent elements
• Strongly pi - regular elements
• Stable range one

Let a be a regular element of a ring R. If either K := r(R) (a) has the exchange property or every power of a is regular, then we prove that for every positive integer n there exist decompositions
R-R = K circle plus X-n circle plus Y-n = E-n circle plus X-n circle plus aY(n).
where Y-n subset of a(n)R and E-n congruent to R/aR. As applications we get easier proofs of the results that a strongly pi-regular ring has stable range one and also that a strongly pi-regular element whose every power is regular is unit-regular.

• 出版日期2016-6