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A ring network is a network topology in which each node connects to exactly two other nodes, forming a single continuous pathway for signals through each node – a ring. Data travels from node to node, with each node along the way handling every packet.
The prime spectrum of a Boolean ring (e.g., a power set ring) is a compact totally disconnected Hausdorff space (that is, a Stone space). [4] (M. Hochster) A topological space is homeomorphic to the prime spectrum of a commutative ring (i.e., a spectral space) if and only if it is compact, quasi-separated and sober. [5]
The generalization of the Zariski topology to the set of prime ideals of a commutative ring follows from Hilbert's Nullstellensatz, that establishes a bijective correspondence between the points of an affine variety defined over an algebraically closed field and the maximal ideals of the ring of its regular functions. This suggests defining the ...
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.
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
One can require either that a presheaf F is a contravariant functor to the category of abelian groups (or rings, or modules, etc.), or that F be an abelian group (ring, module, etc.) object in the category of all contravariant functors from C to the category of sets. These two definitions are equivalent.
Then from each ring, pages of single degree are depicted as hanging downward, with a page linked by the core hanging from the center, for example. In this manner, the rings form a sort of dome away from the center that is reminiscent of a jellyfish, with the hanging nodes making up the creature's tentacles.
PSTN network topology is the switching network topology of a telephone network connected to the public switched telephone network (PSTN).. In the United States and Canada, the Bell System network topology was the switching system hierarchy implemented and operated from c. 1930 to the 1980s for the purpose of integrating the diverse array of local telephone companies and telephone numbering ...