Abstract
The main aim of this paper is to introduce and study the new notions namely M∗-irresolute topological rings and M∗-irresolute topological R-modules by virtue of M∗-open sets. Examples of an M∗-irresolute topological ring and module have been put forth. Further, we provide several fundamental properties and characterizations of M∗-irresolute topological rings and M∗-irresolute topological R-modules. In addition, we shall define boundedness in these two structures and present several results on them.
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