On the locally socle of C(X)C(X)C(X) whose local cozeroset is cocountable (cofinite)

Somayeh SOLTANPOUR

Makale detayları

On the locally socle of C(X)C(X)C(X) whose local cozeroset is cocountable (cofinite)

Yazarlar:

Somayeh SOLTANPOUR

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2019 Vol.48 Issue 5, pp.1430-1436

Belge Tipi:

Makale

Yayın Tarihi:

10/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000451414

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

Özet:

 

Let CF(X)CF(X)C_F(X) be the socle of C(X)C(X)C(X) (i.e., the sum of minimal ideals of C(X)C(X)C(X)). We introduce and study  the concept of colocally socle of C(X)C(X)C(X) as CμSλ(X)={f∈C(X):|X∖Sλf|<μ}CμSλ(X)={f∈C(X):|X∖Sfλ|<μ}C_{\mu}{S_{\lambda}}(X)=\left\{ f\in C(X):|X\backslash {S}^{\lambda}_{f}|<\mu \right\}, where SλfSfλ{{S}^{\lambda}_{f}} is the union of all open subsets UUU in XXX such that |U∖Z(f)|<λ|U∖Z(f)|<λ|U\backslash Z(f)|<\lambda. CμSλ(X)CμSλ(X)C_{\mu}{S_{\lambda}}(X) is a zzz-ideal of C(X)C(X)C(X) containing CF(X)CF(X){{C}_{F}}(X). In particular, Cℵ0Sℵ0(X)=CCF(X)Cℵ0Sℵ0(X)=CCF(X)C_{{\aleph}_0}{S_{{\aleph}_0}}(X)=CC_F(X) and Cℵ1Sℵ1(X)=CSc(X)Cℵ1Sℵ1(X)=CSc(X)C_{{\aleph}_1}{S_{{\aleph}_1}}(X)=CS_c(X) are investigated. For each of the containments in the chain CF(X)⊆CCF(X)⊆CμSλ(X)⊆C(X)CF(X)⊆CCF(X)⊆CμSλ(X)⊆C(X){{C}_{F}}(X)\subseteq CC_F(X)\subseteq C_{\mu}{S_{\lambda}}(X)\subseteq C(X), we characterize the spaces XXX for which the containment is actually an equality. We determine the conditions such that CCF(X)CCF(X)CC_F(X) (CSc(X)CSc(X)CS_c(X)) is not prime in any subrings of C(X)C(X)C(X) which contains the idempotents of C(X)C(X)C(X). The primeness of CCF(X)CCF(X)CC_F(X) in some subrings of C(X)C(X)C(X) is investigated.

Makale detayları

On the locally socle of C(X)C(X)C(X) whose local cozeroset is cocountable (cofinite)

Yazarlar: Somayeh SOLTANPOUR

Yayıncı: Hacettepe University

Ana Başlıklar: Matematik

Dergi: Hacettepe Journal of Mathematics and Statistics 2019 Vol.48 Issue 5, pp.1430-1436

Belge Tipi: Makale

Yayın Tarihi: 10/2019

Belge Dili: İngilizce

Document ID (Org No.): 2000451414

Sıklık: İki Aylık

eISSN: 2651-477X

pISSN: 2651-477X

Sayı

Yazarlar:

Somayeh SOLTANPOUR

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2019 Vol.48 Issue 5, pp.1430-1436

Belge Tipi:

Makale

Yayın Tarihi:

10/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000451414

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X