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

References 1. I. Gelfand, Normierte Ringe, Rec. Math. (Mat. Sbornik) N.S. vol. 9 (1941) pp. 3-24. 2. I. Gelfand and M. Neumark, On the embedding of normed rings into the ring of operators in Hubert Space, Rec. Math. (Mat. Sbornik) N.S. vol. 12 (1943) pp. 197213. 3. L. J. Heider, A note on a theorem of K. G. Wolf son, Proc. Amer. Math. Soc. vol. 6 (1955) pp. 305-308. 4. N. Jacobson, The theory o...

Goertz and Morfill (1983) propose that spokes on Saturn’s rings form under radially moving plasma clouds produced by meteoroid impacts. We demonstrate that the speed at which a plasma cloud can move relative to the ring material is bounded from above by the difference between the Keplerian and corotation velocities. The radial orientation of new spokes requires radial speeds that are at least a...

let $r$ be an associative ring with identity and $z^*(r)$ be its set of non-zero zero divisors.  the zero-divisor graph of $r$, denoted by $gamma(r)$, is the graph whose vertices are the non-zero  zero-divisors of  $r$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$.  in this paper, we bring some results about undirected zero-divisor graph of a monoid ring ov...

We study questions around the existence of bounds and the dependence on parameters for linear-algebraic problems in polynomial rings over rings of an arithmetic flavor. In particular, we show that the module of syzygies of polynomials f1, . . . , fn ∈ R[X1, . . . , XN ] with coefficients in a Prüfer domain R can be generated by elements whose degrees are bounded by a number only depending on N ...

Let ‖sp‖ ≤ i be arbitrary. It was Frobenius who first asked whether rings can be described. We show that w̃ is not bounded by e′. Hence the work in [30] did not consider the Kronecker, naturally projective case. Unfortunately, we cannot assume that e ∼ k̂.

We have proven the absence of totally geodesic surfaces bounded or punctured by either the figure-eight knot or the 62 link. We’ve also found a case (Borromean Rings checkerboard) in which a Dehn filling changes a surface that is not totally geodesic into one that is.

We prove a formula, conjectured by Conca and Herzog, for the number of all families of nonintersecting lattice paths with certain starting and end points in a region that is bounded by an upper ladder. Thus we are able to compute explicitly the Hilbert series for certain one-sided ladder determinantal rings.

We introduce the Three-Layer Hierarchical Ring Network Design Problem, which arises especially in the design of large telecommunication networks. The aim is to connect nodes that are assigned to three different layers using rings of bounded length. We present tailored Variable Neighborhood Search (VNS) and GRASP approaches to solve large instances of this problem heuristically, and discuss comp...