We extend the Gröbner basis theory developed in [10, 11] to certain non-homogeneous, locally filtered finitely generated ideals in R0 , and to certain admissible orders. The main tool used is the study of two homogeneous ideals that may be associated to an ideal I R0 , namely the ideal grT (I) generated by all homogenous components of maximal degree of elements in I , and the “homogenized” idea...

For a commutative ring R, let Nil(R) be the set of all nilpotent elements of R, Z(R) be the set of all zero divisors of R, T (R) be the total quotient ring of R, and H = {R | R is a commutative ring and Nil(R) is a divided prime ideal of R}. For a ring R ∈ H, let φ : T (R) −→ RNil(R) such that φ(a/b) = a/b for every a ∈ R and b ∈ R\Z(R). A ring R is called a ZPUI ring if every proper ideal of R...

For a Hecke pair (G, H) and a character σ of H we consider a generalised Hecke algebra Hσ(G, H), which we study by embedding the given Hecke pair in a Schlichting completion (Gσ, Hσ) that comes equipped with a continuous extension σ on Hσ. The image of σ in Cc(Gσ) is a non-full projection pσ, and Hσ(G, H) is isomorphic to pσCc(Gσ)pσ. We study the structure and properties of C *-completions of a...

since 2005 a new powerful invariant of an algebra has emerged using the earlier work of horvath, hethelyi, kulshammer and murray. the authors studied morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. it was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...

In this paper we prove that Bourgain algebra of qX relative to L? contains C if X is backward shift invariant analytic subalgebra and q ? an inner function, i.e. (qX, L?)b C. We also studied some algebras finitely generated ideals in A H?.

We survey the Stanley-Reisner correspondence in combinatorial commutative algebra, describing fundamental applications involving Alexander duality, associated primes, f and h-vectors, and Betti numbers of monomial ideals.

We describe a recipe for generating normal ideals on successors of singular cardinals. We show that these ideals are related to many weakenings of that have appeared in the literature. Our main purpose, however, is to provide an organized list of open questions related to these ideals. Throughout this note, we will let λ denote the successor of a singular cardinal μ. We will also let χ denote s...