The main theorem gives necessary and sufficient conditions for the rational group algebra QG to be without (nonzero) nilpotent elements if G is a nilpotent or F·C group. For finite groups G, a characterisation of group rings RG over a commutative ring with the same property is given. As ...
A Jordan canonical form for nilpotent elements in an arbitrary ringvon Neumann regularnilpotentJordan canonical formIn this paper we give an inductive new proof of the Jordan canonical form of a nilpotent element in an arbitrary ring. If a is an element of R is a nilpotent element of index ...
skew polynomial ringnilpotent elementsnil-Armendariz ringskew triangular matrix ringWe study the structure of the set of nilpotent elements in extended semicommutative rings and introduce nil u03b1-semicommutative rings as a generalization. We resolve the structure of nil u03b1-semicommutative rings ...
6. Evidence of P-Element-Induced Sister-Chromatid Exchange in a Ring-X Chromosome in Drosophila With Implication for a High Rate of Formation of Hybrid Elements [O] . John A. Sved, Xiumei Liang 2006 机译:在果蝇的Ring-X染色体中P元素诱导的姊妹染色单体交换的证据暗示了杂合元素的高形成率 ...
5) nilpotent elements 幂零元 1. At first,we discuss the Structure of the ring Z/(pm ),namely,the structure and amount of nilpotent elements idempotent elements, invertible elements, zero divisors and ideals in Z/ (pm). 本文先讨论了Z/(pm)环的结构,如其幂零元、幂等元、可逆元、零因子...
Rings whose nilpotent elements form a Levitzki radical ring[J].Communications in algebra 2007,4(4).C. Y. Hong, H. K. Kim, N. K. Kim, T. K. Kwak, Y. Lee, and K. S. Park, Rings whose nilpotent elements form a Levitzki radical ring, Comm. Algebra 35 (2007), no. 4, 1379- ...
In this paper we give a complete classification of the complete K,,-categorical theories of rings with 1 and without nonzero nilpotent elements.It is not feasible to state the main result at the outset, so we simply give a sketch of our analysis.First we show that if A is any ring ...
(3) Let $X$ be a nonempty set and $F$ a field, and let $R = {}^XF$ be the ring of functions $X \rightarrow F$. Prove that $R$ contains no nonzero nilpotent elements. Solution: (1) Suppose $n = a^kb$, where $k \geq 1$. Now $$(ab)^k = a^kb^k = (a^kb)b^{...
6) nilpotent elements 幂零元 1. At first,we discuss the Structure of the ring Z/(pm ),namely,the structure and amount of nilpotent elements idempotent elements, invertible elements, zero divisors and ideals in Z/ (pm). 本文先讨论了Z/(pm)环的结构,如其幂零元、幂等元、可逆元、零因子...
6) nilpotent elements 幂零元 1. At first,we discuss the Structure of the ring Z/(pm ),namely,the structure and amount of nilpotent elements idempotent elements, invertible elements, zero divisors and ideals in Z/ (pm). 本文先讨论了Z/(pm)环的结构,如其幂零元、幂等元、可逆元、零因子...