The prime k-spectrum Speck(R) of a k-semiring R will be introduced. It will be proven that it is a topological space, and some properties of this space will be investigated. Connections between the topological properties of Speck(R) and possible algebraic properties of the k-semiring R will be established.

Let K(n)∗(−) denote the n-th periodic Morava K-theory for any fixed odd prime p. Let k(n) ∗ denote the Ω-spectrum of the n-th connective Morava K-theory. We give a calculation of the Hopf ring K(n)∗k(n) ∗ , the main result of the second author’s thesis. This is a new, shorter, easier proof.

Let G be a finite group. The spectrum of G is the set ω(G) of orders of all its elements. The subset of prime elements of ω(G) is called the prime spectrum ofG and is denoted by π(G). The spectrum ω(G) of a groupG defines its Grunberg–Kegel graph (or prime graph) Γ(G) with vertex set π(G), in which any two different vertices r and s are adjacent if and only if the number rs belongs to the set ω...

Nonstandard mathematics furnishes a remarkable connexion between analytic and algebraic geometry. We describe this interplay for the most basic notions like complex spaces/algebraic schemes, generic points, differential forms etc. We obtain by this point of view in particular new results on the prime spectrum of a Stein algebra. 2000 Mathematics Subject Classification 32C15, 14A15 (primary); 32...

A piggyback duality and a translation process between this one and a Priestley duality for each subvariety of involutive Stone algebras and regular o-De Morgan algebras is presented. As a consequence we describe free algebras and the prime spectrum of each subvariety.

We use Dieudonné theory for periodically graded Hopf rings to determine the Dieudonné ring structure of the Z/2(pn − 1)-graded Morava K-theory K(n)∗(−), with p an odd prime, when applied to the Ω-spectrum k(n) ∗ (and to K(n) ∗ We also expand these results in order to accomodate the case of the full Morava K-theory K(n)∗(−).

— A large class of G-symbolic Morse dynamical systems with simple spectrum is described, where G is a finite, abeban group. The problem of spectral multiplicity in case G == Z^ n is a prime number and x ssb x bx . .. is solved. Some examples of special substitutions having non-homogeneous spectra is presented.

the aim of this short note is to introduce the concepts of prime and semiprime ideals in ordered ag-groupoids with left identity. these concepts are related to the concepts of quasi-prime and quasi-semiprime ideals, play an important role in studying the structure of ordered ag-groupoids, so it seems to be interesting to study them.

the generalized principal ideal theorem is one of the cornerstones of dimension theory for noetherian rings. for an r-module m, we identify certain submodules of m that play a role analogous to that of prime ideals in the ring r. using this definition, we extend the generalized principal ideal theorem to modules.

‎let $g$ be a group with identity $e.$ let $r$ be a $g$-graded‎ ‎commutative ring and $m$ a graded $r$-module‎. ‎in this paper‎, ‎we‎ ‎introduce several results concerning graded classical prime‎ ‎submodules‎. ‎for example‎, ‎we give a characterization of graded‎ ‎classical prime submodules‎. ‎also‎, ‎the relations between graded‎ ‎classical prime and graded prime submodules of $m$ are studied‎.‎