We introduce the notion of strongly ω -Gorenstein modules, where ω is a faithfully balanced self-orthogonal module. This gives a common generalization of both Gorenstein projective (injective) modules and ω-Gorenstein modules. We investigate some characterizations of strongly ω -Gorenstein modules. Consequently, some properties under change of rings are obtained. Keywords—faithfully balanced se...

For prime powers q we use “strongly orthogonal” linear sudoku solutions of order q to construct ordered orthogonal arrays of type OOA(4, s, 2, q), and for each q we present a range of values of s for which these constructions are valid. These results rely strongly on flags of subspaces in a four dimensional vector space over a finite field.