‎‎Let $R$ be a commutative ring with identity and let $M$ be an $R$-module‎. ‎We define the primary spectrum of $M$‎, ‎denoted by $mathcal{PS}(M)$‎, ‎to be the set of all primary submodules $Q$ of $M$ such that $(operatorname{rad}Q:M)=sqrt{(Q:M)}$‎. ‎In this paper‎, ‎we topologize $mathcal{PS}(M)$ with a topology having the Zariski topology on the prime spectrum $operatorname{Spec}(M)$ as a sub...

We construct the centralizer resolution of the spectrum EhS 1 2 in the category of K(2)-local spectra at the prime 2. We use the associated tower of fibrations to realize the duality resolution to a tower of fibrations whose limit is the spectrum EhS 1 2 . We also compute the Adams-Novikov spectral sequence for the spectrum tmf without assuming the ring structure on the spectrum and compute π∗E...

In this paper we defined prime ideal and maximal ideal and proved several properties of these. We have discussed the space of prime ideals of a C-algebra A with respect to the hull-kernel topology, which is called the prime spectrum of A and denoted by Spec A. It is also proved that Spec A is a T0 space.

We find the nonabelian finite simple groups with order prime divisors not exceeding 1000. More generally, we determine the sets of nonabelian finite simple groups whose maximal order prime divisor is a fixed prime less than 1000. Our results are based on calculations in the computer algebra system GAP.