Jordan and associative rings with nilpotent and invertible elements

Nilpotent Elements in Skew Polynomial Rings

 Letbe a ring with an endomorphism and an -derivationAntoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. In this paper we introduce and investigate the notion of nil--compatible rings. The class of nil--compatible rings are extended through various ring extensions and many classes of nil--compatible rings are constructed. We al...

Lie and Jordan Structures in Simple, Associative Rings

On One-sided Lie Nilpotent Ideals of Associative Rings

We prove that a Lie nilpotent one-sided ideal of an associative ring R is contained in a Lie solvable two-sided ideal of R. An estimation of derived length of such Lie solvable ideal is obtained depending on the class of Lie nilpotency of the Lie nilpotent one-sided ideal of R. One-sided Lie nilpotent ideals contained in ideals generated by commutators of the form [. . . [[r1, r2], . . .], rn−1...

Invertible and Nilpotent Matrices over Antirings

Abstract. In this paper we characterize invertible matrices over an arbitrary commutative antiring S with 1 and find the structure of GLn(S). We find the number of nilpotent matrices over an entire commutative finite antiring. We prove that every nilpotent n×n matrix over an entire antiring can be written as a sum of ⌈log2 n⌉ square-zero matrices and also find the necessary number of square-zer...

Invertible Rings and Axiomatic Algebra

Assume λ ≥ 0. Every student is aware that Ω > 0. We show that ε(Yβ,ψ) ∈ YC ,l. Thus the work in [14] did not consider the Smale case. Thus this could shed important light on a conjecture of Poisson.