let ( r,m ) be a noetherian local ring, a an ideal of r and m a finitely generated r- module. we investigate some properties of formal local cohomology modules with respect to a serre subcategory. we provide a common language to indicate some properties of formal local cohomology modules. let ( r,m ) be a noetherian local ring, a an ideal of r and m a finitely generated r- module. we investigat...

This paper seeks ring-theoretic conditions of an integral domain R that reflect in the Clifford property or Boolean property of its class semigroup S(R), that is, the semigroup of the isomorphy classes of the nonzero (integral) ideals of R with the operation induced by multiplication. Precisely, in Section 3, we characterize integrally closed domains with Boolean class semigoup; in this case, S...

known as the left big finitistic projective dimension of A, is finite. Here pdM denotes the projective dimension of M . Unfortunately, this number is not known to be finite even if A is a finite dimensional algebra over a field, where, indeed, its finiteness is a celebrated conjecture. On the other hand, for such an algebra, finite flat certainly implies finite projective dimension, simply beca...

We present several results related to van Douwen’s Problem, which asks whether there is homogeneous compactum with cellularity exceeding c, the cardinality of the reals. For example, just as all known homogeneous compacta have cellularity at most c, they satisfy similar upper bounds in terms of Peregudov’s Noetherian type and related cardinal functions defined by order-theoretic base properties...

Resco and Small gave the first example of an affine Noetherian algebra which is not finitely presented. It shown that their has no finite-dimensional filtrations whose associated graded algebras are Noetherian, affirming prediction. A modification yields countable fields over ‘almost all’ (that is, a co-countable continuum of) lack such filtration, answer to question suggested by Irving derived.

Abstract In this paper, we prove that a classical theorem by McAdam about the analytic spread of an ideal in Noetherian local ring continues to be true for divisorial filtrations on two-dimensional normal excellent R , and Hilbert polynomial fiber cone filtration has function which is sum linear bounded function. We these theorems first studying asymptotic properties divisors resolution singula...

in 2001, s. bulman-fleming et al. initiated the study of three flatness properties (weakly kernel flat, principally weakly kernel flat, translation kernel flat) of right acts $a_{s}$ over a monoid $s$ that can be described by means of when the functor $a_{s} otimes -$ preserves pullbacks. in this paper, we extend these results to$s$-posets and present equivalent descriptions of weakly kernel po...

We prove that every regular Gaussian polynomial over a locally Noetherian ring has invertible content ideal. We do this by first proving that Gaussian polynomials over an approximately Gorenstein local ring have principal content ideal. We also show over locally Noetherian rings that a regular polynomial f of degree n is Gaussian if c(fg) = c(f)c(g) for polynomials g of degree at most n. Introd...