Iranian Journal of Mathematical Sciences and Informatics مجله علوم ریاضی و انفورماتیک IJMSI Basic Sciences http://ijmsi.ir 1 admin 1735-4463 2008-9473 8 10.29252/ijmsi 14 8888 13 en jalali 1399 1 1 gregorian 2020 4 1 15 1 online 1 fulltext
en Sums of Strongly z-Ideals and Prime Ideals in \${mathcal{R}} L\$ تخصصي Special پژوهشي Research paper <p style="margin: 0px;">It is well-known that the sum of two \$z\$-ideals in \$C(X)\$ is either \$C(X)\$ or a \$z\$-ideal.</p> <p style="margin: 0px;">The main aim of this paper is to study the sum of strongly \$z\$-ideals in \${mathcal{R}} L\$, the ring of real-valued continuous functions on a frame \$L\$.</p> <p style="margin: 0px;">For every ideal \$I\$ in \${mathcal{R}} L\$, we introduce the biggest strongly \$z\$-ideal included in \$I\$ and the smallest strongly \$z\$-ideal containing \$I\$,</p> <p style="margin: 0px;">denoted by \$I^{sz}\$ and \$I_{sz}\$, respectively.</p> <p style="margin: 0px;">We study some properties of \$I^{sz}\$ and \$I_{sz}\$. &nbsp;</p> <p style="margin: 0px;">Also, it is observed that the sum of any family of minimal prime ideals in the ring \${mathcal{R}} L\$ is either \${mathcal{R}} L\$ or a prime strongly \$z\$-ideal in \${mathcal{R}} L\$.</p> <p style="margin: 0px;">In particular, we show that the sum of two prime ideals in \${mathcal{R}} L\$ such that are not a chain, is a prime strongly \$z\$-ideal.</p> Frame, Ring of real-valued continuous functions, z-Ideal, Strongly z-ideal. 23 34 http://ijmsi.ir/browse.php?a_code=A-10-2462-1&slc_lang=en&sid=1 A. A. Estaji aaestaji@gmail.com `10031947532846006957` 10031947532846006957 Yes Hakim Sabzevari University Hakim Sabzevari University A. Karimi Feizabadi akarimi@gorganiau.ac.ir `10031947532846006958` 10031947532846006958 No Islamic Azad University Islamic Azad University M. Robat Sarpoushi M.sarpooshi@yahoo.com `10031947532846006959` 10031947532846006959 No Hakim Sabzevari University Hakim Sabzevari University