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A characterization of weakly J(n)-rings

Danchev P. V.

Journal of Mathematics and Applications

2018

Vol. 41

53--61

A ring R is called a J(n)-ring if there exists a natural number n ≥ 1 such that for each element r ∈ R the equality r (n+1) = r holds and a weakly J(n)-ring if there exists a natural number n ≥ 1 such that for each element r ∈ R the equalities r (n+1) = r or r(n+1) = -r hold. We completely describe both classes of these rings R for any n, thus considerably extending some well-known results in the subject, especially that of V. Perić in Publ. Inst. Math. Beograd (1983) as well as, in particular, the classical description of Boolean rings when n = 1.

Semiprime FDI-rings

Gubareni N.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 4

49--59

In this paper we present some results for FDI-rings, i.e. rings with a complete set of pairwise orthogonal primitive idempotents. We consider the nilpotency index of ideals and give its upper band for ideals in some classes of rings. We also give a new proof of a criterion of semiprime FDI-rings to be prime.

A classification of cube radical zero completely primary finite rings

Chikunji Ch. J.

Demonstratio Mathematica

2005

Vol. 38, nr 1

7--20

In this paper, we consider the isomorphism problem of a class of completely primary finite rings R such that if M. is the Jacobson radical of R, thenM3 = (0) and M2 = (0), in the general case (not necessarily the case where the maximal Galois subrings lie in the center). We further obtain the number of non-isomorphic classes in a special case of these rings.

A note on p-injectivity

Yue Chi Ming R.

Demonstratio Mathematica

2004

Vol. 37, nr 1

45--54

This note contains results related to p-injectivity and YJ-injectivity. Conditions are given for rings to be (i) V-rings; (ii) VNR; (iii) self-injective regular or strongly regular. A characterization of principal ideal quasi-Frobenius rings is given in terms of p-injectivity. A condition is given for a fully right idempotent ring to have a von Neumann regular classical left quotient ring. It is also proved that if A is a fully right idempotent, right Goldie ring, then every two-sided ideal of A is generated by a central idempotent.