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In this work, we present a standard model for Galois rings based on the standard model of their residual fields, that is, a sequence of Galois rings starting with ${mathbb Z}_{p^r} that coves all the Galois rings with that characteristic ring and such that there is an algorithm producing each member of the sequence whose input is the size of the required ring.
A theory of monoids in the category of bicomodules of a coalgebra $C$ or $C$-rings is developed. This can be viewed as a dual version of the coring theory. The notion of a matrix ring context consisting of two bicomodules and two maps is introduced a
The recently developed theory of Schur rings over a finite cyclic group is generalized to Schur rings over a ring R being a product of Galois rings of coprime characteristics. It is proved that if the characteristic of R is odd, then as in the cyclic
The results of [I. Ojeda, Amer. Math. Monthly, 122, pp 60--64] provides a characterization of Kronecker square roots of matrices in terms of the symmetry and rank of the block vec matrix (rearrangement matrix). In this short note we reformulate the c
In this note, we show that a strongly $phi$-ring $R$ is a $phi$-PvMR if and only if any $phi$-torsion free $R$-module is $phi$-$w$-flat, if and only if any divisible module is nonnil-absolutely $w$-pure module, if and only if any $h$-divisible module
We provide a formula for commputing the discriminant of skew Calabi-Yau algebra over a central Calabi-Yau algebra. This method is applied to study the Jacobian and discriminant for reflection Hopf algebras.