In this article we investigate subring growth of Z for small n using p-adic integration. To the memory of Fritz Grunewald

In this paper, various elementary properties of vague rings are obtained. Furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

The notion of an interval-valued (∈,∈ ∨q)-fuzzy subring(ideal,prime) in ring is introduced and their characterizations are investigated. Mathematics Subject Classification: 03E72,16D25

We show that prime Fano threefolds $Y$ of genus 8 have a multiplicative Chow–Künneth decomposition, in the sense Shen–Vial. As consequence, certain tautological subring Chow ring powers injects into cohomology.

We show that Gushel-Mukai fivefolds admit a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As consequence, certain tautological subring Chow ring powers these varieties injects into cohomology.

Let X be a topological space and R be a subring of RX. By determining some special topologies on X associated with the subring R, characterizations of maximal fixxed and maximal growing ideals in R of the form Mx(R) are given. Moreover, the classes of zR-ideals and z0R-ideals are introduced in R which are topological generalizations of z-ideals and z0-ideals of C(X), respectively. Various c...

We provide a first order axiomatization of the expansion of the complex field by the exponential function restricted to the subring of integers modulo the first order theory of (Z, +, ·). 2000 Mathematics Subject Classification: 03C60