‎‎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 $h^2(l‎, ‎c^*) cong m(l)$‎...

We mainly investigate the structures of skew cyclic and skew quasicyclic codes of arbitrary length over Galois rings. Similar to [5], our results show that the skew cyclic codes are equivalent to either cyclic and quasi-cyclic codes over Galois rings. Moreover, we give a necessary and sufficient condition for skew cyclic codes over Galois rings to be free. A sufficient condition for 1-generator...

In this paper we generalize coding theory of cyclic codes over finite fields to skew polynomial rings over finite rings. Codes that are principal ideals in quotient rings of skew polynomial rings by two sided ideals are studied. Next we consider skew codes of endomorphism type and derivation type. And we give some examples. Mathematics Subject Classification: Primary 94B60; Secondary 94B15, 16D25

In this paper we generalize coding theory of cyclic codes over finite fields to skew polynomial rings over finite rings. Codes that are principal ideals in quotient rings of skew polynomial rings by two sided ideals are studied. Next we consider skew codes of endomorphism type and derivation type. And we give some examples.

We characterize skew polynomial rings and power series that are reduced right or left Archimedean.