On self-injectivity of the $f$-ring ${\Frm(\mathcal{P}(\mathbb{R}),L)}$

Rok, strany: 2019, 999 - 1008

Let $\mathcal{F}_{\mathcal P}L:=\Frm(\mathcal{P}(\mathbb R), L)$. We show that if $L$ is a $P$-frame then $\mathcal{F}_{\mathcal P}L$ is an $\aleph₀$-self-injective ring. We prove that a zero-dimensional frame $L$ is extremally disconnected if and only if $\mathcal{F}_{\mathcal P}L$ is a self-injective ring. Finally, it is shown that $\mathcal{F}_{\mathcal P}L$ is a Baer ring if and only if $\mathcal{F}_{\mathcal P}L$ is a continuous ring if and only if $\mathcal{F}_{\mathcal P}L$ is a complete ring if and only if $\mathcal{F}_{\mathcal P}L$ is a $CS$-ring.

ISO 690:

Estaji, A., Abedi, M., Darghadam, A. 2019. On self-injectivity of the $f$-ring ${\Frm(\mathcal{P}(\mathbb{R}),L)}$. In Mathematica Slovaca, vol. 69, no.5, pp. 999-1008. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0284

APA:

Estaji, A., Abedi, M., Darghadam, A. (2019). On self-injectivity of the $f$-ring ${\Frm(\mathcal{P}(\mathbb{R}),L)}$. Mathematica Slovaca, 69(5), 999-1008. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0284

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava