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Primary components of binomial ideals

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  1. Tez No: 401318
  2. Yazar: ZEKİYE ESER
  3. Danışmanlar: DR. LAURA F. MATUSEVICH
  4. Tez Türü: Doktora
  5. Konular: Matematik, Mathematics
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 2014
  8. Dil: İngilizce
  9. Üniversite: Texas A&m Unıversıty
  10. Enstitü: Yurtdışı Enstitü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: Belirtilmemiş.

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Özet (Çeviri)

Binomials are polynomials with at most two terms. A binomial ideal is an ideal generated by binomials. Primary components and associated primes of a binomial ideal are still binomial over algebraically closed elds. Primary components of general binomial ideals over algebraically closed elds with characteristic zero can be described combinatorially by translating the operations on binomial ideals to operations on exponent vectors. In this dissertation, we obtain more explicit descriptions for primary components of special binomial ideals. A feature of this work is that our results are independent of the characteristic of the eld. First of all, we analyze the primary decomposition of a special class of binomial ideals, lattice ideals, in which every variable is a nonzerodivisor modulo the ideal. Then we provide a description for primary decomposition of lattice ideals in elds with positive characteristic. In addition, we study the codimension two lattice basis ideals and we compute their primary components explicitly. An ideal I „ krx1; :::; xns is cellular if every variable is either a nonzerodivisor modulo I or is nilpotent modulo I. We characterize the minimal primary components of cellular binomial ideals explicitly. Another signi cant result is a computation of the Hull of a cellular binomial ideal, that is the intersection of all of its minimal primary components. Lastly, we focus on commutative monoids and their congruences. We study properties of monoids that have counterparts in the study of binomial ideals. We provide a characterization of primary ideals in positive characteristic, in terms of the congruences they induce.

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