MSc.Thesis Defense: Erdem Şafak Öztürk

 ALGEBRAIC AND COMBINATORIAL PROPERTIES OF t-SPREAD IDEALS

Erdem Şafak Öztürk
Mathematics, MSc. Thesis, 2024

Thesis Jury

Asst. Prof. Ayesha Asloob Qureshi (Thesis Advisor),

Asst. Prof.  Nurdagül Anbar,

 Assoc. Prof. Roghayeh Hafezieh

Date & Time: 17th, 2024 –  11:00 AM

Place: FENS L063

Keywords : t-spread monomial ideals, strongly stable ideals, Borel ideals, t-spread Veronese ideals, Rees algebras of t-spread ideals

Abstract

In this thesis, we study t-spread strongly stable monomial ideals. It is proved that for an ideal to be t-spread strongly stable, it is sufficient for the definition criterion to be satisfied only on its minimal monomial generating set. The generators, height, Cohen-Macaulayness, and minimal free resolution of some special classes of t-spread strongly stable monomial ideals, namely,

t-spread Veronese ideals and t-spread principal Borel ideals and their Alexander dual are studied. We also study the Rees algebras of t-spread principal Borel ideals, and it is shown that they have the so-called l-exchange property. Consequently, the Rees algebra of a t-spread principal Borel ideal is Koszul.