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

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.

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

maximal submodule , max-injective module , max-spectral space , multiplication module , Zariski topology