Two notes on “On the maximal spectrum of a module and Zariski topology”

Document Type : Research Paper

Authors

Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People's Republic of Korea

Abstract

For unitary modules over commutative rings with non-zero identity, Question 3.28 in [Bull. Malays. Math. Sci. Soc. 38(1) (2015) 303] asks if the maximal spectrum of a max-injective module is a max-spectral topological space and Proposition 3.19 in it contains an assertion that the maximal spectrum of a max-injective module is a T2-space. In this paper, we give a negative answer to the above question and show that the above assertion is false by two examples of multiplication modules.

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Journal of Algebra and Related Topics
Volume 12, Issue 2
January 2025
Pages 47-51

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