A quintuple quotient quest

The Quest for Quotient Rings (Of Noncommutative Noetherian Rings)

Articles on the history of mathematics can be written from many different perspectives. Some aim to survey a more or less wide landscape, and require the observer to watch from afar as theories develop and movements are born or become obsolete. At the other extreme, there are those that try to shed light on the history of particular theorems and on the people who created them. This article belo...

Linear quintuple-product identities

In the first part of this paper, series and product representations of four single-variable triple products T0, T1, T2, T3 and four single-variable quintuple products Q0, Q1, Q2, Q3 are defined. Reduced forms and reduction formulas for these eight functions are given, along with formulas which connect them. The second part of the paper contains a systematic computer search for linear trinomial ...

On Graphical Quintuple Systems

It is well-known that the following divisibility conditions are necessary for the existence of a t-(v, k, A) design: A(V-~) == 0 mod (k~), Os; i:::; t. t-, t-, A t.( v, k, A) design (0, £ilJ) with £ilJ =0 or ffi=Lk(n) is said to be trivial. One can show by elementary counting arguments that in a trivial t-(v, k,A) design, we must have either A=0 or A = (k=:)' The complement of a t.(v, k, A) des...

Asymptomatic synchronous quintuple primary cancers.

We encountered a 46-year-old woman with synchronous quintuple primary cancers. She did not present with any symptoms, and her tumors were discovered at a gynecological screening. She had clear cell adenocarcinoma of the right ovary, moderately differentiated endometrioid adenocarcinoma of the endometrium, moderately differentiated adenocarcinoma of the ascending colon, well-differentiated adeno...

A Note on Strongly Quotient Graphs