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A new and stronger central sets theorem

Dibyendu De;  Neil Hindman;  Dona Strauss — 2008

Fundamenta Mathematicae

Furstenberg's original Central Sets Theorem applied to central subsets of ℕ and finitely many specified sequences in ℤ. In this form it was already strong enough to derive some very strong combinatorial consequences, such as the fact that a central subset of ℕ contains solutions to all partition regular systems of homogeneous equations. Subsequently the Central Sets Theorem was extended to apply to arbitrary semigroups and countably many specified sequences. In this paper we derive a new version...

An interesting class of ideals in subalgebras of C ( X ) containing C * ( X )

Sudip Kumar Acharyya;  Dibyendu De — 2007

Commentationes Mathematicae Universitatis Carolinae

In the present paper we give a duality between a special type of ideals of subalgebras of C ( X ) containing C * ( X ) and z -filters of β X by generalization of the notion z -ideal of C ( X ) . We also use it to establish some intersecting properties of prime ideals lying between C * ( X ) and C ( X ) . For instance we may mention that such an ideal becomes prime if and only if it contains a prime ideal. Another interesting one is that for such an ideal the residue class ring is totally ordered if and only if it is prime.

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