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Token Ring (802.5) networks imitate a ring at layer 2 but use a physical star at layer 1. "Rings prevent collisions." The term "ring" only refers to the layout of the cables. It is true that there are no collisions on an IBM Token Ring, but this is because of the layer 2 Media Access Control method, not the physical topology (which again is a ...
Thus π is injective if and only if this intersection reduces to the zero element of the ring; by the Krull intersection theorem, this is the case for any commutative Noetherian ring which is an integral domain or a local ring. There is a related topology on R-modules, also called Krull or I-adic topology.
Download as PDF; Printable version ... ring theory is the study ... the spectrum of a commutative ring is the space of its prime ideals equipped with Zariski topology
A network's logical topology is not necessarily the same as its physical topology. For example, the original twisted pair Ethernet using repeater hubs was a logical bus topology carried on a physical star topology. Token Ring is a logical ring topology, but is wired as a physical star from the media access unit.
Ethernet Ring Protection Switching (ERPS) is an effort at ITU-T under G.8032 Recommendation to provide sub-50ms protection and recovery switching for Ethernet traffic in a ring topology and at the same time ensuring that there are no loops formed at the Ethernet layer.
In algebraic geometry, especially when R is the local ring of a scheme at some point P, R / m is called the residue field of the local ring or residue field of the point P. If (R, m) and (S, n) are local rings, then a local ring homomorphism from R to S is a ring homomorphism f : R → S with the property f(m) ⊆ n. [5]
The group of units of a topological ring is a topological group when endowed with the topology coming from the embedding of into the product as (,). However, if the unit group is endowed with the subspace topology as a subspace of , it may not be a topological group, because inversion on need not be continuous with respect to the subspace topology.
Visualization of an all-to-all algorithm in a ring topology. Visualization of an all-to-all algorithm in a mesh topology. We consider a single-ported machine. The way the data is routed through the network depends on its underlying topology. We take a look at all-to-all algorithms for common network topologies.