5 Hopf Rings 11 5.1 What is a Hopf ring? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2 DS as a co-Hopf ring spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 5.3 Rational Morava E-theory of DS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 6 EDS is a formal power series ring under ? 12 6.1 Determining...

We discuss the determination of the radius of the total graph of a commutative ring R in the case when this graph is connected. Typical extensions such as polynomial rings, formal power series, idealization of the R-module M and relations between the total graph of the ring R and its extensions are also dealt with.

Motivated by recent works on the genus of classifying spaces of compact Lie groups, here we study the set of filtered λ-ring structures over a filtered ring from a purely algebraic point of view. From a global perspective, we first show that this set has a canonical topology compatible with the filtration on the given filtered ring. For power series rings R[[x]], where R is between Z and Q, wit...

Let $R$ be a strongly $\mathbb {Z}^2$ -graded ring, and let $C$ bounded chain complex of finitely generated free -modules. The is $R_{(0,0)}$ -finitely dominated, or type $FP$ over , if it homotopy equivalent to projective We show that this happens only becomes acyclic after taking tensor product with certain eight rings formal power series, the graded analogues classical Novikov rings. This ex...

When [Formula: see text] is a finite field, [J. Becker, J. Denef and L. Lipshitz, Further remarks on the elementary theory of formal power series rings, in Model Theory Algebra Arithmetic, Proceedings Karpacz, Poland, Lecture Notes Mathematics, Vol. 834 (Springer, Berlin, 1979)] observed that total residue map text], which picks out constant term Laurent series, definable language rings with pa...