Two finite Alexander quandles with the same number of elements are isomorphic iff their Z[t]-submodules Im(1 − t) are isomorphic as modules. This yields specific conditions on when Alexander quandles of the form Zn[t ]/(t − a) where gcd(n, a) = 1 (called linear quandles) are isomorphic, as well as specific conditions on when two linear quandles are dual and which linear quandles are connected. ...

for a fixed positive integer , we say a ring with identity is n-generalized right principally quasi-baer, if for any principal right ideal of , the right annihilator of is generated by an idempotent. this class of rings includes the right principally quasi-baer rings and hence all prime rings. a certain n-generalized principally quasi-baer subring of the matrix ring are studied, and connections...

A new method for realizing the first and second order cohomology groups of an internal abelian group in a Barr-exact category was introduced in [6] and [10]. The main role, in each level, is played by a direction functor. This approach can be generalized to any level n and produces a long exact cohomology sequence. By applying this method to Moore categories we show that they represent a good c...