In this paper, we consider flat epimorphisms of commutative rings [Formula: see text] such that, for every ideal which text], the quotient ring is semilocal Krull dimension zero. Under these assumptions, show that projective R-module U does not exceed 1. We also describe Geigle–Lenzing perpendicular subcategory in text]. Assuming additionally and all are perfect, R-modules U-strongly flat. Thus...

Let H denote a finite simple hypergraph. The cover ideal of H, denoted by J = J(H), is the monomial ideal whose minimal generators correspond to the minimal vertex covers of H. We give an algebraic method for determining the chromatic number of H, proving that it is equivalent to a monomial ideal membership problem involving powers of J . Furthermore, we study the sets Ass(R/Js) by exploring th...

We use hypersurface support to classify thick (two-sided) ideals in the stable categories of representations for several families finite-dimensional integrable Hopf algebras: bosonized quantum complete intersections, Borels type $A$, Drinfeld doubles height 1 finite characteristic, and rings functions on group schemes over a perfect field. then identify prime ideal (Balmer) spectra these catego...

A new way of constructing (minimal) perfect hash functions is described. The technique considerably reduces the overhead associated with resolving buckets in two-level hashing schemes. Evaluating a hash function requires just one multiplication and a few additions apart from primitive bit operations. The number of accesses to memory is two, one of which is to a fixed location. This improves the...

We consider the problem of covering the complete r-uniform hypergraphs on n vertices using complete r-partite graphs. We obtain lower bounds on the size of such a covering. For small values of r our result implies a lower bound of Ω( e r r √ r n log n) on the size of any such covering. This improves the previous bound of Ω(rn log n) due to Snir [5]. We also obtain good lower bounds on the size ...

In this paper, we consider the iterated trimming complex associated to data yielding a of length 3. We compute an explicit algebra structure in terms structures input data. Moreover, it is shown that many these products become trivial after descending homology. apply results problem realizability for Tor-algebras grade 3 perfect ideals, and show under mild hypotheses, process “trimming” ideal p...

Abstract It is proved that a map ${\varphi }\colon R\to S$ of commutative Noetherian rings essentially finite type and flat locally complete intersection if only $S$ proxy small as bimodule. This means the thick subcategory generated by module over enveloping algebra $S\otimes _RS$ contains perfect complex supported fully on diagonal ideal. in spirit classical result }$ smooth bimodule; to say,...

Existing Global Data Computation (GDC) protocols for asynchronous systems are round-based algorithms designed for fully connected networks. In this paper, we discuss GDC in asynchronous chordal rings, a nonfully connected network. The virtual links approach to solve the consensus problem may be applied to GDC for non-fully connected networks, but it incurs high message overhead. To reduce the o...

Let S be a polynomial algebra over field. If I is the edge ideal of perfect semiregular tree, then we give precise formulas for values depth, Stanley projective dimension, regularity and Krull dimension S/I.