Associated to each set S of simple roots for SL(n, C) is an equivariant fibration X → XS of the space X of complete flags of C n. To each such fi-bration we associate an algebra JS of operators on L 2 (X) which contains, in particular, the longitudinal pseudodifferential operators of negative order tangent to the fibres. These form a lattice of operator ideals whose common intersection is the c...

We characterize those intersection-type theories which yield complete intersection-type assignment systems for λ-calculi, with respect to the three canonical set-theoretical semantics for intersection-types: the inference semantics, the simple semantics and the F-semantics.

‎Let $R$ be a commutative ring with non-zero identity. ‎We describe all $C_3$‎- ‎and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. ‎Also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎Finally, ‎we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. ...

We compute the arithmetic ranks of the defining ideals of homogeneous coordinate rings of certain Segre products arising from elliptic curves. The cohomological dimension of these ideals varies with the characteristic of the field, though the arithmetic rank does not. We also study the related set-theoretic Cohen-Macaulay property for these ideals. In [12] Lyubeznik writes: Part of what makes t...

Problem and motivation. A static type system can be an extremely powerful tool for a programmer, providing early error detection, and offering strong compile-time guarantees on the behavior of a program. However, compared to dynamic typing, static typing often comes at the expense of development speed and flexibility, as statically-typed code might be more difficult to adapt to changing require...

Let R be a ring with unity and I(R) be the set of all non-trivial left ideals of R. The intersection graph of ideals of R, denoted by G(R), is a graph with the vertex set I(R) and two distinct vertices I and J are adjacent if and only if I ∩ J 6= 0. In this paper, we study some connections between the graph-theoretic properties of this graph and some algebraic properties of rings. We characteri...