Affectionately dedicated to Mel Hochster, who has been an inspiration to us for many years, on the occasion of his 65th birthday. Abstract We study the fibers of projective morphisms and rational maps. We characterize the analytic spread of a homogeneous ideal through properties of its syzygy matrix. Powers of linearly presented ideals need not be linearly presented, but we identify a weaker li...

A toroidalization of a dominant morphism $varphi: Xto Y$ of algebraic varieties over a field of characteristic zero is a toroidal lifting of $varphi$ obtained by performing sequences of blow ups of nonsingular subvarieties above $X$ and $Y$. We give a proof of toroidalization of locally toroidal morphisms of 3-folds.

We show that for an artin algebra Λ, the telescope conjecture for module categories is equivalent to certain idempotent ideals of modΛ being generated by identity morphisms. As a consequence, we prove the conjecture for domestic standard selfinjective algebras and domestic special biserial algebras. We achieve this by showing that in any Krull-Schmidt category with local d.c.c. on ideals, any i...

Let us suppose every Riemann, arithmetic, algebraically complex ideal is prime and almost everywhere bijective. In [35, 40], the authors address the integrability of non-holomorphic manifolds under the additional assumption that M̄ ≤ Q . We show that a′ ∈ π. Now we wish to extend the results of [35] to Taylor morphisms. Unfortunately, we cannot assume that there exists a super-Lambert injective,...

This paper continues the functional approach to the P-versus-NP problem, begun in [1]. Here we focus on the monoid RM 2 of right-ideal morphisms of the free monoid, that have polynomial input balance and polynomial time-complexity. We construct a machine model for the functions in RM 2 , and evaluation functions. We prove that RM 2 is not finitely generated, and use this to show separation resu...

We define a class of productive σ−ideals of subsets of the Cantor space 2ω and observe that both σ−ideals of meagre sets and of null sets are in this class. From every productive σ−ideal J we produce a σ−ideal Jκ of subsets of the generalized Cantor space 2κ. In particular, starting from meagre sets and null sets in 2ω we obtain meagre sets and null sets in 2κ, respectively. Then we investigate...

This paper is an exposition of the so-called injective Morita contexts (in which the connecting bimodule morphisms are injective) and Morita α-contexts (in which the connecting bimodules enjoy some local projectivity in the sense of ZimmermannHuisgen). Motivated by situations in which only one trace ideal is in action, or the compatibility between the bimodule morphisms is not needed, we introd...

in this paper, we introduce a new generalization of weakly prime ideals called $i$-prime. suppose $r$ is a commutative ring with identity and $i$ a fixed ideal of $r$. a proper ideal $p$ of $r$ is $i$-prime if for $a, b in r$ with $ab in p-ip$ implies either $a in p$ or $b in p$. we give some characterizations of $i$-prime ideals and study some of its properties.  moreover, we give conditions  ...

We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the null ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler’s classical result in the theory of forcing, and the stat...