The Hopkins-Mahowald theorem realizes the Eilenberg-Maclane spectra $H\mathbb F_p$ as Thom for all primes $p\in\mathbb N_{>0}$. In this article, we record a known proof of generalization theorem, realizing $Hk$ perfect rings $k$, and provide further by $HR$ perfectoid $R$. We also discuss even generalizations to prisms $(A,I)$ indicates how adapt our proofs Breuil-Kisin case.

A Computational Theory of Laurent Polynomial Rings and Multidimensional FIR Systems by HYUNG-JU PARK Doctor of Philosophy in Mathematics University of California at Berkeley A Laurent polynomial ring is a natural ground ring for the study of FIR (Finite Impulse Response) systems in signal processing since an FIR lter bank can be seen as a matrix over this ring, and the notion of perfect reconst...

We introduce the notion of a coordinate k ${\bf k}$ -algebra scheme and corresponding B $\mathcal {B}$ -operator. This class operators includes endomorphisms derivations Frobenius map, it generalizes related to D {D}$ -rings from Moosa Scanlon (J. Math. Log. 14 (2014), no. 02, 1450009) as well. classify (coordinate) schemes for perfect field we also discuss model-theoretic properties fields wit...

let $r$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $r$ and $f(x)=a_0+a_1x+cdots+a_nx^n$ be a nonzero skew polynomial in $r[x;alpha]$. it is proved that if there exists a nonzero skew polynomial $g(x)=b_0+b_1x+cdots+b_mx^m$ in $r[x;alpha]$ such that $g(x)f(x)=c$ is a constant in $r$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $r$ such tha...

we observe some new characterizations of $n$-presented modules. using the concepts of $(n,0)$-injectivity and $(n,0)$-flatness of modules, we also present some characterizations of right $n$-coherent rings, right $n$-hereditary rings, and right $n$-regular rings.

in this paper, we introduce the concept of the   generalized aip-rings as a generalization of the generalized quasi-   baer rings   and generalized p.p.-rings. we show that the class of the generalized aip-rings is closed under direct products and morita invariance. we also characterize the 2-by-2 formal upper triangular matrix rings of this new class of rings. finally, we provide sever...

this paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

We consider the Coulomb drag between two metal rings in which the longrange Coulomb interaction leads to the formation of a Wigner crystal. The first ring is threaded by an Aharanov–Bohm flux, creating a persistent current J0. The second ring is brought into close proximity to the first and due to the Coulomb interaction between the two rings a drag current JD is produced in the second. We inve...

The unusual aromatic stability of cyclic bicalicene has been suggested to come from a tetraionic structure, where positive and negative charges are located on the cyclopropene and cyclopentadiene rings, respectively. Energetic, magnetic, geometric and electron delocalization analysis performed on a series of bicalicene derivatives, incorporating different electron donating and withdrawing group...

We identify a self-enforcing collusion protocol (a “bidding ring”) for non-repeated first-price auctions. Unlike previous work on the topic such as that by McAfee and McMillan [1992] and Marshall and Marx [2007], we allow for the existence of multiple cartels in the auction and do not assume that non-colluding agents have perfect knowledge about the number of colluding agents whose bids are sup...