Abstract We construct a Leray model for discrete polymatroid with arbitrary building set and we prove generalized Goresky–MacPherson formula. The first row of the is Chow ring polymatroid; Poincaré duality, Hard Lefschetz, Hodge–Riemann theorems ring. Furthermore, provide relative Lefschetz decomposition respect to deletion an element.

We show spherical completeness of the ring of Colombeau generalized real numbers endowed with the sharp norm. As an application, we establish a Hahn-Banach extension theorem for ultra-pseudo-normed modules of generalized functions in the sense of Colombeau.

We prove that a generalized periodic, as well as a generalized Boolean, ring is either commutative or periodic. We also prove that a generalized Boolean ring with central idempotents must be nil or commutative. We further consider conditions which imply the commutativity of a generalized periodic, or a generalized Boolean, ring. 2000 Mathematics Subject Classification. 16D70, 16U80. Throughout,...

the role of some ring structures in the distribution of porphyry copper deposits in south kerman porphyry copper belt is discussed. in the study area, ring structures are circular or elliptical shaped features which are partly recognized on satellite images. in this study, landsat multispectral images were used to identify ring structures in the area. the rudimentary identification stages of th...

Generalized Cox’s construction associates with an algebraic variety a remarkable invariant – its total coordinate ring, or Cox ring. In this note we give a new proof of factoriality of the Cox ring when the divisor class group of the variety is finitely generated and free. The proof is based on a notion of graded factoriality. We show that if the divisor class group has torsion, then the Cox ri...