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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.

Regular elements and Green's relations in power Menger algebras of terms

Denecke K., Glubudom P.

Demonstratio Mathematica

2008

Vol. 41, nr 1

11-22

Sets of terms of type r are called tree languages (see [5]). On sets of tree languages superposition operations can be defined in such a way that the collection of all tree languages of type r forms an abstract clone. Considering only sets of n-ary terms one obtains a Menger algebra (see e.g. [3]). From the superposition operations binary operations on tree languages can be derived. For the corresponding sernigroups of tree languages we study idempotent and regular elements as well as Green's relations L and R.