We show that a properly stratified algebra is Gorenstein if and only the characteristic tilting module coincides with cotilting module. further algebras A enjoy strong homological properties such as all projective modules being endomorphism rings End ( Δ i ) Frobenius algebras. apply our results to study of are minimal Auslander-Gorenstein in sense Iyama-Solberg calculate under suitable conditi...

We show that for a large class of rings R, the number principally polarized abelian varieties over finite field in given simple ordinary isogeny and with endomorphism ring R is equal either to 0, or ratio numbers associated up some small computable factors. This includes maximal order CM K (for which result was already known), as well generated Z by Frobenius Verschiebung.

we give a new proof of the well known wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎we apply the concept of frobenius kernel in frobenius representation theorem in finite group‎ ‎theory to build a proof‎.

MacWilliams’ equivalence theorem states that Hamming isometries between linear codes extend to monomial transformations of the ambient space. One of the most elegant proofs for this result is due to K. P. Bogart et al. (1978, Inform. and Control 37, 19–22) where the invertibility of orthogonality matrices of finite vector spaces is the key step. The present paper revisits this technique in orde...