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...

In the title compound, C(18)H(17)FO(2)S, the 4-fluoro-phenyl ring is almost perpendicular to the benzofuran fragment [88.07 (5)°]. The crystal structure exhibits weak inter-molecular C-H⋯O hydrogen bonds and C-H⋯π inter-actions. The mol-ecules form pseudo-helices along the a axis.

In this paper the concept of an $Omega$- Almost Boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $Omega$- Almost Boolean ring over a locally Boolean space.

We investigate Hermitian forms on finitely generated torsion modules over a noncommutative discrete valuation ring. We also give some results for lattices, which still are satisfied even if the base ring is not commutative. Moreover, for a noncommutative discrete-valued division algebra D with valuation ring R and residual division algebra D̄, we prove that W(D̄) ∼=WT(R), where WT(R) denotes the ...