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.