With every $R$-module $M$ associate the direct limit of $\Hom_R (D, M)$ over the dense right ideals of $R$, the derived quotient module $\mathcal{D}(M)$ of $M ...

Transactions of the American Mathematical Society, Vol. 359, No. 12 (Dec., 2007), pp. 6027-6055 (29 pages) We initiate a study of Hilbert modules over the polynomial algebra ${\cal A}=ℂ[z_{1},...,z_{d ...

Algebraic structures such as semirings and modules have long been a fertile ground for both theoretical exploration and practical application. Semirings, generalisations of rings that typically lack ...