XX\mathfrak{X}-elements in  multiplicative lattices - A generalization of JJJ-ideals, nnn-ideals and rrr-ideals in rings

Sachin SARODE; Vinayak JOSHI

doi:https://doi.org/10.24330/ieja.1102289

Makale detayları

XX\mathfrak{X}-elements in multiplicative lattices - A generalization of JJJ-ideals, nnn-ideals and rrr-ideals in rings

Yazarlar:

Sachin SARODE | Vinayak JOSHI

Yayıncı:

Abdullah HARMANCI

Ana Başlıklar:

Matematik

Dergi:

International Electronic Journal of Algebra 2022 Vol.32 Issue 32, pp.46-61

Belge Tipi:

Makale

Yayın Tarihi:

7/2022

Belge Dili:

İngilizce

Document ID (Org No.):

2000717749

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

https://doi.org/10.24330/ieja.1102289

Özet:

 

In this paper, we introduce the concept of an XX\mathfrak{X}-element with respect to an MMM-closed set XX\mathfrak{X} in multiplicative lattices and study properties of XX\mathfrak{X}-elements. For a particular MMM-closed subset XX\mathfrak{X}, we define the concepts of rrr-elements, nnn-elements and JJJ-elements. These elements generalize the notion  of rrr-ideals, nnn-ideals and JJJ-ideals of a commutative ring with identity to multiplicative lattices. In fact, we prove that an ideal III of a commutative ring RRR with identity is a nnn-ideal (JJJ-ideal) of RRR if and only if it is an nnn-element (JJJ-element) of Id(R)Id(R)Id(R), the ideal lattice of RRR.

Makale detayları

XX\mathfrak{X}-elements in multiplicative lattices - A generalization of JJJ-ideals, nnn-ideals and rrr-ideals in rings

Yazarlar: Sachin SARODE | Vinayak JOSHI

Yayıncı: Abdullah HARMANCI

Ana Başlıklar: Matematik

Dergi: International Electronic Journal of Algebra 2022 Vol.32 Issue 32, pp.46-61

Belge Tipi: Makale

Yayın Tarihi: 7/2022

Belge Dili: İngilizce

Document ID (Org No.): 2000717749

Sıklık: Aylık

eISSN: 1306-6048

pISSN: 1306-6048

DOI: https://doi.org/10.24330/ieja.1102289

Sayı

Yazarlar:

Sachin SARODE | Vinayak JOSHI

Yayıncı:

Abdullah HARMANCI

Ana Başlıklar:

Matematik

Dergi:

International Electronic Journal of Algebra 2022 Vol.32 Issue 32, pp.46-61

Belge Tipi:

Makale

Yayın Tarihi:

7/2022

Belge Dili:

İngilizce

Document ID (Org No.):

2000717749

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

https://doi.org/10.24330/ieja.1102289