Abstract : In this paper, a criterion for normality of a family of meromorphic functions involving differential polynomials is obtained which generalizes a result of Deng et al (J. Aust. Math. Soc. 91(2011), 313-322). As a consequence, a counterexample to the converse of Bloch's principle is also obtained. In addition, we prove some normality criterion generalizing a result of Chen et al (Acta Math. Sci. 36(2016), 87-93). Wherever possible, examples are provided to demonstrate sharpness of results.
Abstract : This article introduces the concept of weakly quasi-$S$-primary ideals, which generalize both weakly $S$-primary and quasi-$S$-primary ideals. We define an ideal $P$ of a ring $R$ to be weakly quasi-$S$-primary if there exists $s \in S$ such that, for all $x, y \in R$, if $0 \neq xy \in P$, then either $sx \in \sqrt{P}$ or $sy \in \sqrt{P}$. We investigate various properties and characterizations of weakly quasi-$S$-primary ideals, and provide numerous examples and counterexamples. We also study the behavior of these ideals under homomorphisms, in rings of fractions, in idealizations, and in amalgamated rings.
Ismael Akray, Amin Mahamad Zebari
Commun. Korean Math. Soc. 2023; 38(1): 21-38
https://doi.org/10.4134/CKMS.c210349
Vinay Kumar, Rajendra Prasad, Sandeep Kumar Verma
Commun. Korean Math. Soc. 2023; 38(1): 205-221
https://doi.org/10.4134/CKMS.c210433
Harish Chandra, Anurag Kumar Patel
Commun. Korean Math. Soc. 2023; 38(2): 451-459
https://doi.org/10.4134/CKMS.c220108
Anjan Kumar Bhuniya, Manas Kumbhakar
Commun. Korean Math. Soc. 2023; 38(1): 1-9
https://doi.org/10.4134/CKMS.c210057
Vinay Kumar, Rajendra Prasad, Sandeep Kumar Verma
Commun. Korean Math. Soc. 2023; 38(1): 205-221
https://doi.org/10.4134/CKMS.c210433
Ismael Akray, Amin Mahamad Zebari
Commun. Korean Math. Soc. 2023; 38(1): 21-38
https://doi.org/10.4134/CKMS.c210349
Anjan Kumar Bhuniya, Manas Kumbhakar
Commun. Korean Math. Soc. 2023; 38(1): 1-9
https://doi.org/10.4134/CKMS.c210057
Traiwat Intarawong, Boonrod Yuttanan
Commun. Korean Math. Soc. 2023; 38(2): 355-364
https://doi.org/10.4134/CKMS.c220139
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