Strict Shells

  • Arthur Knoebel


The hypothesis that shells be Baer–Stone is rather restrictive. We weaken it, but to obtain a theorem comparable to that of the previous chapter, we must also weaken the previous conclusion: the representation is only as a subalgebra of the algebra of all global sections of a sheaf, rather than as an isomorphic image. The stalks still have no divisors of zero.The first section proves the theorem just summarized, for algebras that have only a multiplication and a nullity, called strict half-shells. We assume these half-shells have no nilpotents and satisfy null-symmetry, a collection of implications between products that are zero.The second section starts by exploring the consequence of having no divisors of zero when the sheaf is a Boolean product: the enveloping half-shell is then Baer–Stone. When the sheaf space is extremal disconnected, the enveloping half-shell is completely Baer–Stone.The third section adds a unity and an addition that is loop to the half-shell; this makes for stronger and simpler conclusions. We apply it to clusters.


Prime Ideal Commutative Ring Factor Ideal Ring Theory Regular Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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