We construct a nil ring R which has bounded index of nilpotence 2, is Wedderburn radical, and is commutative, and which also has a derivation δ for which the differential polynomial ring R[x; δ] is not even prime radical. This example gives a strong barrier to lifting certain radical properties from rings to differential polynomial rings. It also demarcates the strength of recent results about ...

We construct some explicit formulas of rational maps and transcendental meromorphic functions having Herman rings period strictly larger than one. This gives an answer to a question raised by Shishikura in the 1980s. Moreover, with nested are also found. To obtain periodic rings, crucial step is find family entire bounded Siegel disks all possible periods rotation numbers. based on proving exis...

We call a graded connected algebra R effectively coherent, if for every linear equation over R with homogeneous coefficients of degrees at most d, the degrees of generators of its module of solutions are bounded by some function D(d). For commutative polynomial rings, this property has been established by Hermann in 1926. We establish the same property for several classes of noncommutative alge...

We study the language-theoretical aspects of parameterized communicating automata (PCAs), in which processes communicate via rendez-vous. A given PCA can be run on any topology of bounded degree such as pipelines, rings, ranked trees, bus topologies, and grids. We show that, under a context bound, which restricts the local behavior of each process, PCAs are effectively complementable. Complemen...

an r-module m is called epi-retractable if every submodule of mr is a homomorphic image of m. it is shown that if r is a right perfect ring, then every projective slightly compressible module mr is epi-retractable. if r is a noetherian ring, then every epi-retractable right r-module has direct sum of uniform submodules. if endomorphism ring of a module mr is von-neumann regular, then m is semi-...

‎‎we exhibit an explicit construction for the second cohomology group‎ ‎$h^2(l‎, ‎a)$ for a lie ring $l$ and a trivial $l$-module $a$‎. ‎we show how the elements of $h^2(l‎, ‎a)$ correspond one-to-one to the‎ ‎equivalence classes of central extensions of $l$ by $a$‎, ‎where $a$‎ ‎now is considered as an abelian lie ring‎. ‎for a finite lie‎ ‎ring $l$ we also show that $h^2(l‎, ‎c^*) cong m(l)$‎...

Let $R$ be a strongly $\mathbb {Z}^2$ -graded ring, and let $C$ bounded chain complex of finitely generated free -modules. The is $R_{(0,0)}$ -finitely dominated, or type $FP$ over , if it homotopy equivalent to projective We show that this happens only becomes acyclic after taking tensor product with certain eight rings formal power series, the graded analogues classical Novikov rings. This ex...