For a top semimodule over semiring with zero and nonzero identity, this paper studies the interplay between topological properties of subtractive prime spectrum algebraic semimodule. We prove that subtractively finitely generated is compact space, establish necessary sufficient conditions for to be generated. For
 multiplication commutative semiring, we radical subsemimodule coincides its ...

It is shown that a commutative Bézout ring R with compact minimal prime spectrum is an elementary divisor ring if and only if so is R/L for each minimal prime ideal L. This result is obtained by using the quotient space pSpec R of the prime spectrum of the ring R modulo the equivalence generated by the inclusion. When every prime ideal contains only one minimal prime, for instance if R is arith...

Given an elliptic fibration $f \colon X \to S$ over the spectrum of a complete discrete valuation ring with algebraically closed residue field, we use Hochschild--Serre spectral sequence to express torsion in $R^1f_\ast \mathscr{O}_X$ as first group cohomology $H^1(G,H^0(S^\prime, \mathscr{O}_{S^\prime}))$. Here, $G$ is Galois maximal extension $K^\prime / K$ such that normalization $X \times_S...

This paper studies a fascinating type of filter in residuated lattices, the so-called pure filters. A combination algebraic and topological methods on filters lattice is applied to obtain some new structural results. The notion purely-prime has been investigated, Cohen-type theorem obtained. It shown that spectrum compact sober space, Grothendieck-type demonstrated. proved Gelfand Hausdorff ded...

Abstract We present a $$q_T$$ q T -resummed calculation of diphoton production at order N $$^3$$ 3 LL $$^\prime $$ ? + NNLO. To reach the primed level accuracy we have implemented recently published t...