Ay Saylam, Başak

Profile URL
https://hdl.handle.net/11147/15881
Name Variants
Ay, Basak
Saylam, Başak Ay
Saylam, Basak Ay
Saylamo, Basak A. Y.
Saylamo, Başak A. Y.
Ay, Başak
Ay Saylam, Basak
Job Title
Email Address
basakay@iyte.edu.tr
Main Affiliation
04.02. Department of Mathematics
Status
Current Staff
Website
http://web.iyte.edu.tr/~basakay/
ORCID ID
0000-0003-3448-2776
Scopus Author ID
56121697700
Turkish CoHE Profile ID
Google Scholar ID
78EZ_L8AAAAJ
WoS Researcher ID
C-2119-2014

Sustainable Development Goals

SDG data is not available
Documents

12

Citations

14

h-index

2

Go to Scopus profile
Documents

9

Citations

5

Go to WoS profile
Scholarly Output

14

Articles

10

Views / Downloads

27617/3222

Supervised MSc Theses

3

Supervised PhD Theses

1

WoS Citation Count

5

Scopus Citation Count

6

Patents

0

Projects

2

WoS Citations per Publication

0.36

Scopus Citations per Publication

0.43

Open Access Source

10

Supervised Theses

4

JournalCount
Communications in Algebra4
Turkish Journal of Mathematics3
Journal of Algebra and its Applications2
Proceedings of the Indian Academy of Sciences: Mathematical Sciences1
Current Page: 1 / 1

Scopus Quartile Distribution

Competency Cloud

GCRIS Competency Cloud

Filters

2014 - 201972020 - 20247

Settings

search.filters.applied.f.isAuthorOfPublication: search.filters.isAuthorOfPublication.17e5299e-1d6a-4e13-880c-b9eb5e1c4b2c

Scholarly Output Search Results

Now showing 1 - 10 of 14
  • Article
    Citation - Scopus: 2
    On Density Theorems for Rings of Krull Type With Zero Divisors
    (TUBITAK, 2014) Ay Saylam, Başak
    Let R be a commutative ring and I(R) denote the multiplicative group of all invertible fractional ideals of R, ordered by A ≥ B if and only if B ⊆ A. If R is a Marot ring of Krull type, then R(Pi), where {Pi}i∈I are a collection of prime regular ideals of R, is a valuation ring and R = ∩ R(Pi) . We denote by Gi the value group of the valuation associated with R(Pi). We prove that there is an order homomorphism from I(R) into the cardinal direct sum ∐i∈I Gi and we investigate the conditions that make this monomorphism onto for R.
  • Doctoral Thesis
    Krull-Schmidt Properties Over Non-Noetherian Rings
    (Izmir Institute of Technology, 2022) Gürbüz, Ezgi; Ay Saylam, Başak
    Let R be a commutative ring and C a class of indecomposable R-modules. The Krull-Schmidt property holds for C if, whenever G1 ⊕ ·· · ⊕ Gn H1 ⊕ ·· · ⊕ Hm for Gi, Hj ∈ C, then n = m and, after reindexing, Gi Hi for all i ≤ n. The main purpose of this thesis is to investigate Krull-Schmidt properties of certain classes of modules over Non-Noetherian rings. Particularly weakly Matlis domains, strong Mori domains and Marot rings, all of which are among the class of Non-Noetherian rings, are studied. wweak isomorphism types are defined and the conditions when they coincide for torsionless modules over weakly Matlis domains are discussed. With the help of this comparison, the Krull-Schmidt property of w-ideals of a strong Mori domain is characterized. Also, the same property for overrings of a strong Mori domain is examined. Some useful results for a Marot ring with ascending condition on its regular ideals are obtained. Krull-Schmidt property on regular ideals of such a ring is studied and a characterization is given. Furthermore, the same property is discussed for overrings of a Marot ring.
  • Article
    Locally Isomorphic Torsionless Modules Over Domains of Finite Character
    (World Scientific Publishing, 2019) Saylam, Başak Ay; Klingler, Lee
    In a 2002 paper, P. Goeters and B. Olberding compare local, near, and stable isomorphisms of torsionless modules over h-local domains. In this paper, we compare these weaker forms of isomorphisms of torsionless modules over domains of finite character.
  • Article
    Unique decompositions into regular ideals for Marot rings
    (Taylor & Francis, 2022) Ay Saylam, Başak; Gürbüz, Ezgi
    Let R be a commutative ring. We say that R has the unique decomposition into regular ideals (UDRI) property if, for any R-module which decomposes into a finite direct sum of regular ideals, this decomposition is unique up to the order and isomorphism class of the regular ideals. In this paper, we will prove some preliminary results for Marot rings whose regular ideals are finitely generated and give a necessary and sufficient condition for these rings to satisfy the UDRI property.
  • Article
    W-Locally Isomorphic Torsionless Modules Over Weakly Matlis Domains
    (Taylor & Francis inc, 2024) Ay Saylam, Basak; Gurbuz, Ezgi; Hamdi, Haleh
    Let R be an integral domain. An R-module G is torsionless if it is isomorphic to a submodule of a finitely generated free R-module. For torsionless modules, we define w-weak isomorphism types which are new versions of weak isomorphism types with respect to the w-operation: w-local isomorphism and w-nearly isomorphism. Furthermore, we examine the relationship between w-local isomorphism, w-nearly isomorphism, and stable isomorphism for torsionless w-modules over weakly Matlis domains.
  • Master Thesis
    Almost Local-Global Rings
    (Izmir Institute of Technology, 2017) Susuzlu, İdem; Ay Saylam, Başak
    The main purpose of this thesis is to investigate the Invariant Factor Theorem for Prüfer domains. In accordance with this aim, we give a survey of necessary and su cient conditions on a Prüfer domain to satisfy the Invariant Factor Theorem. In this process, almost local-global rings have important role since they satisfy the USC-property. Regarding to the UCS-property, BCS-rings together with their properties are also investigeted.
  • Article
    Citation - WoS: 1
    Corrigendum: on Density Theorems for Rings of Krull Type With Zero Divisors
    (TUBITAK, 2017) Ay Saylam, Başak
    This corrigendum is written to correct some parts of the paper "On density theorems for rings of Krull type with zero divisors". The proofs of Proposition 2.4 and Proposition 4.3 are incorrect and the current note makes the appropriate corrections.
  • Article
    The Group of Invertible Ideals of a Prufer Ring
    (Indian Academy of Sciences, 2020) Saylam, Başak Ay
    Let R be a commutative ring and I( R) denote the multiplicative group of all invertible fractional ideals of R, ordered by A <= B if and only if B subset of A. We investigatewhen there is an order homomorphism from I(R) into the cardinal direct sum G(i), where G(i)'s are value groups, if R is a Marot Prufer ring of finite character. Furthermore, over Prufer rings with zero-divisors, we investigate the conditions that make this monomorphism onto.
  • Master Thesis
    Approximation Theorems for Krull Domains
    (Izmir Institute of Technology, 2014) Yeşil, Mehmet; Ay Saylam, Başak
    Let R be an integrally closed domain, and denote by I(R) the multiplicative group of all invertible fractional ideals of R. Let {Vi}i∈I be the family of valuation overrings of R, and denote by Gi the corresponding value group of the valuation domain Vi. We show that R = Ti∈I Vi, and there is a map from I(R) into Qi∈I Gi, the cardinal product of the Gi’s. Furthermore, it is well known when R is a Dedekind domain, this map becomes an isomorphism onto `i∈I Gi, the cardinal sum of the Gi’s. In this case, Gi ∼= Z for each i. It is shown, by J. Brewer and L. Klingler, that this map is also an isomorphism onto`i∈I Gi when R is an h-local Prüfer domain. In this thesis, we investigate the existence of such a map, and whether it is injective when R is a Krull domain.
  • Article
    Es-W
    (Taylor & Francis, 2021) Ay Saylam, Başak; Hamdi, Haleh
    We introduce and study the notion of ES-w-stability for an integral domain R. A nonzero ideal I of R is called ES-w-stable if (I-2)(w) = (JI)(w) for some t-invertible ideal J of R contained in I, and I is called weakly ES-w-stable if I-w = (JE)(w) for some t-invertible fractional ideal J of R and w-idempotent fractional ideal E of R. We define R to be an ES-w-stable domain (resp., a weakly ES-w-stable domain) if every nonzero ideal of R is ES-w-stable (resp., weakly ES-w-stable). These notions allow us to generalize some well-known properties of ES-stable and weakly ES-stable domains.