Results 11 to 20 of about 1,178 (260)
Rings virtually satisfying a polynomial identity [PDF]
Journal of Pure and Applied Algebra, 2005 Let \(f(x_1,\dots,x_n)\) be a nonzero polynomial without constant term in the free associative ring \(\mathbb{Z}\langle x_1,x_2,\dots\rangle\). A ring \(R\) is called an \(f\)-ring if it satisfies the polynomial identity \(f=0\); it is a virtual \(f\)-ring if for every \(n\) infinite subsets \(X_1,\dots,X_n\) of \(R\) there exist \(r_i\in X_i\) such ...
Abdollahi, Alireza, Akbari, Saieed
openaire +2 more sources
Eulerian Polynomial Identities on Matrix Rings [PDF]
Journal of Algebra, 1993 It is well known that the Amitsur-Levitzki theorem can be proved using some graph-theoretical constructions, see, e.g. \textit{R. G. Swan} [Proc. Am. Math. Soc. 14, 367-373 (1963; Zbl 0118.018)]. The paper under review is a further development in this direction. Assume \(G\) is an Eulerian directed graph having \(k\) vertices and \(N\) edges, and let \(
Szigeti, Jenő +2 more
openaire +3 more sources
Polynomial identities that imply commutativity for rings [PDF]
Linear Algebra and its Applications, 2002 The authors consider polynomial identities of the form \(P=Q\), where \(P\) and \(Q\) are monic monomials in two variables that have the same degree in each variable, and that are distinct in the noncommutative associative case. They first show that if both \(P\) and \(Q\) have degree 3, then any 2-torsion free ring with 1 that satisfies \(P=Q\) is ...
Takagi, Hiroyuki +2 more
openaire +2 more sources
On Semiprime Noetherian PI-Rings [PDF]
, 2000 Let R be a semiprime Noetherian PI-ring and Q(R) the semisimple Artinian ring of fractions of R. We shall prove the following conditions are equivalent: (1) the Krull dimention of R is at most one, (2) Any ring between R and Q(R) is again right ...
Chiba, Katsuo
core +1 more source
, 2002 The main concern of this book is the study of Smarandache analogue properties of near-rings and Smarandache near-rings; so it does not promise to cover all concepts or the proofs of all ...
Vasantha, Kandasamy
core +1 more source
, 2002 Over the past 25 years, I have been immersed in research in Algebra and more particularly in ring theory. I embarked on writing this book on Smarandache rings (Srings) specially to motivate both ring theorists and Smarandache algebraists to develop and ...
Vasantha, Kandasamy
core +1 more source
Group rings satisfying a polynomial identity
Journal of Algebra, 1972 D S Passman
exaly +2 more sources
Regular self-injective rings with a polynomial identity [PDF]
, 1974 This paper studies maximal quotient rings of semiprime P. I.-rings; such rings are regular, self-injective and satisfy a polynomial identity. We show that the center of a regular self-injective ring is regular self-injective; this enables us to establish
Stuart A. Steinberg +1 more
core +1 more source
Affine polynomial identity rings and their generalizations
Journal of Algebra, 1979 Amiram Braun
exaly +2 more sources
Generalized Derivations with Commutativity and Anti-commutativity Conditions [PDF]
, 2007 Let R be a prime ring with 1, with char(R) ≠ 2; and let F : R → R be a generalized derivation. We determine when one of the following holds for all x,y ∈ R: (i) [F(x); F(y)] = 0; (ii) F(x)ΟF(y) = 0; (iii) F(x) Ο F(y) = x Ο
Rehman, Nadeem-ur +3 more
core +1 more source