We are applying a new approach to interpret the generalized version of order 8 mock theta functions [Formula: see text] and [Formula: see text] in terms of [Formula: see text]-color partitions. In literature, we find the interpretations of these functions in terms of split [Formula: see text]-color partitions and signed partitions. In addition, we are interpreting the generalized versions of two mock theta functions of order 6 and two of order 5 in terms of [Formula: see text]-color partitions. A mock theta function of order 3 is interpreted in terms of [Formula: see text]-color partitions. We further extend our results using lattice paths.
In this paper we introduce the notions of soft intersectional ternary subsemirings and soft intersectional ideals in ternary semirings. We also discuss some basic results associated with these notions. In the last part of the paper we characterize regular and weakly regular ternary semirings by their soft intersectional ideals.
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