Extensions of Schur’s irreducibility results

Generalizations of some irreducibility results by Schur

Finiteness Results for Hilbert’s Irreducibility Theorem

Let k be a number field, Ok its ring of integers, and f(t,X) ∈ k(t)[X] be an irreducible polynomial. Hilbert’s irreducibility theorem gives infinitely many integral specializations t 7→ t̄ ∈ Ok such that f(t̄, X) is still irreducible. In this paper we study the set Redf (Ok) of those t̄ ∈ Ok with f(t̄, X) reducible. We show that Redf (Ok) is a finite set under rather weak assumptions. In particular...

Some new results on Borel irreducibility of equivalence relations ∗

We prove that orbit equivalence relations (ERs, for brevity) of generically turbulent Polish actions are not Borel reducible to ERs of a family which includes Polish actions of S∞, the group of all permutations of N, and is closed under the Fubini product modulo the ideal Fin of all finite sets, and some other operations. Our second main result shows that T2, an equivalence relation called “the...

extensions, minimality and idempotents of certain semigroup compactifications

در فصل اول مقدمات و پیش نیازهای لازم برای فصل های بعدی فراهم گردیده است . در فصل دوم مساله توسیع مورد توجه قرار گرفته و ابتدا شرایطی که تحت آن از یک فشرده سازی نیم گروهی خاص یک زیرگروه نرمال بسته یک گروه به یک فشرده سازی متناظر با فشرده سازی اولیه برای گروه رسید مورد بررسی قرار گرفته و سپس ارتیاط بین ساختارهای مختلف روی این دو فشرده سازی از جمله ایده آل های مینیمال چپ و راست و... مورد بررسی قرا...

Clique Irreducibility and Clique Vertex Irreducibility of Graphs

A graphs G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and is clique reducible if it is not clique irreducible. A graph G is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G and clique vertex reducible if it is not clique vertex irreducible. The clique vertex irred...