A note on non-commutative semigroups
A note on orthodox additive inverse semirings
We show in an additive inverse regular semiring with as the set of all multiplicative idempotents and as the set of all additive idempotents, the following conditions are equivalent: (i) For all , implies . (ii) is orthodox. (iii) is a semilattice of groups. This result generalizes the corresponding result of regular ring.
A note on -adic completion of torsion-free abelian groups
A note on -solvable and solvable finite groups.
A note on ....-permutable semigroups.
A note on principal ideals and -classes in the direct product of two semigroups
A note on probabilistic representations of operator semigroups.
A note on products of infinite cyclic groups
A note on pseudo-symmetric numerical semigroups.
A note on quasi and bi-duals in ternary semigroups.
A note on quasi-splitting of abelian groups
A note on radicals in a class of semigroups
A note on radicals in regular semigroups.
A Note on Radicals of Semigroups
A note on regular semigroups with inverse transversals.
A note on representations of the finite Heisenberg group and sums of greatest common divisors.
A note on r-extensible prefix codes.
A note on -groupoids
A note on semilattice decompositions of completely -regular semigroups.
A note on semilocal group rings
Let be an associative ring with identity and let denote the Jacobson radical of . is said to be semilocal if is Artinian. In this paper we give necessary and sufficient conditions for the group ring , where is an abelian group, to be semilocal.