zR-Ideals and z R-Ideals in Subrings of RX

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Rezaei Aliabad Ali; Parsinia Mehdi

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Journal Paper

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Journal: Iranian Journal of Mathematical Sciences and Informatics Year:2019 | Volume:14 | Issue:1 Page(s): 55-67

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Information Journal Paper

Title

zR-Ideals and z R-Ideals in Subrings of RX

Author(s)

Rezaei Aliabad Ali | Parsinia Mehdi | Issue Writer Certificate

Keywords

Z(R)

topology

Coz(R)

topology

ideal

zR

ideal

vertible subring

Abstract

Let X be a topological space and R be a subring of RX. By determining some special topologies on X associated with the subring R, characterizations of maximal fixed and maximal g-ideals in R of the form Mx(R) are given. Moreover, the classes of Z(R)-ideals and z R-ideals are introduced in R which are topological generalizations of z-ideals and z-ideals of C(X), respectively. Various characterizations of these ideals are established. Also, coincidence of Z(R)-ideals with z-ideals and z R-ideals with z-ideals in R are investigated. It turns out that some fundamental statements in the context of C(X) are extended to the subrings of RX.

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APA: Copy

Rezaei Aliabad, Ali, & Parsinia, Mehdi. (2019). zR-Ideals and z R-Ideals in Subrings of RX. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), 14(1), 55-67. SID. https://sid.ir/paper/310481/en

Vancouver: Copy

Rezaei Aliabad Ali, Parsinia Mehdi. zR-Ideals and z R-Ideals in Subrings of RX. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)[Internet]. 2019;14(1):55-67. Available from: https://sid.ir/paper/310481/en

IEEE: Copy

Ali Rezaei Aliabad, and Mehdi Parsinia, “zR-Ideals and z R-Ideals in Subrings of RX,” IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), vol. 14, no. 1, pp. 55–67, 2019, [Online]. Available: https://sid.ir/paper/310481/en

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