A commutative ring R is said to satisfy property (P) if every finitely generated proper ideal of R admits a non-zero annihilator. In this paper we give some necessary and sufficient conditions that a ring satisfies property (P). In particular, we characterize coherent rings, noetherian rings and P-coherent rings with property (P).

We exhibit an example of a line bundle M on a smooth complex projective variety Y s.t. M satisfies Property Np for some p, the p-module of a minimal resolution of the ideal of the embedding of Y by M is nonzero and M does not satisfy Property Np. Let M be a very ample line bundle on a smooth complex projective variety Y and let φM : Y → P(H (Y,M)) be the map associated to M . We recall the defi...

We prove that for every finite dimensional compact metric space X there is an open continuous linear surjection from Cp[0, 1] onto Cp(X). The proof makes use of embeddings introduced by Kolmogorov and Sternfeld in connection with Hilbert’s 13th problem.

The notion of strong p-Helly hypergraphs was introduced by Golumbic and Jamison in 1985 [M.C. Golumbic, R.E. Jamison, The edge intersection graphs of paths in a tree, J. Combin. Theory Ser. B 38 (1985) 8–22]. Independently, other authors [A. Bretto, S. Ubéda, J. Žerovnik, A polynomial algorithm for the strong Helly property. Inform. Process. Lett. 81 (2002) 55–57, E. Prisner, Hereditary clique-...

In this paper we prove the universal property of skew PBW extensions generalizing this way the well known universal property of skew polynomial rings. For this, we will show first a result about the existence of this class of non-commutative rings. Skew PBW extensions include as particular examples Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Art...

Proof-supported logical verification of program properties has been a topic of research interest for more than 30 years. The feasibility of proof construction as a verification technique has been demonstrated through many examples of its application, yet it remains a technique rarely used in practice for a variety of reasons, both technical and sociological. The lack of verification logics for ...

The pioneering work of Mumford ([M]), its amplifications by St. Donat ([SD]) and Fujita ([F]), the inspiring work of Green ([Gr]), followed by works of Green and Lasarsfeld ([G-L]) and Ein and Lasarsfeld ([E-L]), have captured the interest and have influenced a large number of researchers in the last fifteen years. Several authors have studied the defining equations of projective varieties and,...

The purpose of this note is to prove the conjecture. The ingredients of the argument are: (a) Taubes’ theorem [11] on the non-vanishing of the SeibergWitten invariants for symplectic 4-manifolds; (b) the theorem of Gabai [7] on the existence of taut foliations on 3-manifolds with non-zero betti number; (c) the construction of Eliashberg and Thurston [4], which produces a contact structure from ...