Let [Formula: see text] be a commutative ring with identity, multiplicatively closed subset of text], and an text]-module. A submodule is called coidempotent if text]. Also, fully every coidempotent. In this paper, we introduce the concepts text]-coidempotent submodules text]-modules as generalizations text]-modules. We explore some basic properties these classes

Developing the calculation techniques to fivefold heavy hadrons, we perform study of novel fully $QQQQ\overline{Q}$ pentaquark states by QCD sum rule approach that is firmly based on basic theory. Numerically, masses are calculated be ${7.41}_{\ensuremath{-}0.31}^{+0.27}\text{ }\text{ }\mathrm{GeV}$ for $cccc\overline{c}$ and ${21.60}_{\ensuremath{-}0.22}^{+0.73}\text{ $bbbb\overline{b}$, respe...