For an algebraic number field k and a prime p, define the number p to be the maximal number d such that there exists a Galois extension of k whose Galois group is a free pro-p-group of rank d. The Leopoldt conjecture implies 1~ p ~ r2 +1, (r2 denotes the number of complex places of k). Some examples of k and p with 03C1 = r2 + 1 have been known so far. In this note, the invariant 03C1 is studie...

Consider a non-commutative algebraic surface, X, and an effective divisor Y on X, as defined by Van den Bergh. We show that the Riemann-Roch theorem, the genus formula, and the self intersection formula from classical algebraic geometry generalize to this setting. We also apply our theory to some special cases, including the blow up of X in a point, and show that the self intersection of the ex...

LetM be a smooth oriented manifold. The homology ofM has the structure of a Frobenius algebra. This paper shows that on chain level there is a Frobenius-like algebra structure, whose homology gives the Frobenius algebra of M . Moreover, associated to any Frobeniuslike algebra, there is a chain complex whose homology has the structure of a Gerstenhaber algebra and a Batalin-Vilkovisky algebra. A...

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A mathematical framework which has been speci cally developed for manufacturing-like systems is presented, focusing on time-free dynamics and control, as treated by Finite State Automata. The approach is based on the key concepts of object types, locations and manufacturing operations enriched with an algebra (Manufacturing Algebra) for building complex operations as algebraic series-parallel c...

This paper provides an algebraic background for the formal derivation of greedy-like algorithms. Such derivations have previously been done in various frameworks including relation algebra. We propose Kleene algebra as a particularly simple alternative. Instead of converse and residuation we use modal operators that are definable in a wide class of algebras, based on domain/codomain or image/pr...