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In this paper we introduce the concept of half-groups. This is a totally new concept and demands considerable attention.

Shyam Sunder Gupta [3] has de ned Smarandache consecutive and reversed Smarandache sequences of triangular numbers. Del m F.M.Torres and Viorica Teca [1] havefurther investigated these sequences and de ned mirror and symmetric Smarandache sequencesof triangular numbers making use of Maple system. Working on the same lines we have dened and investigated consecutive, reversed, mirror and symmetric Smarandache sequencesof pentagonal numbers of dimension 2 using the Maple system .

In this paper, we have introduced Smarandache quasigroups which are Smaran- dache non-associative structures. W.B.Kandasamy [2] has studied Smarandache groupoidsand Smarandache semigroups etc. Substructure of Smarandache quasigroups are also studied.

G. Pilz [1] has de ned near-rings and semi-near-rings. In this paper we introduce the concepts of quasi-near ring and semiquasi-near ring. We have also de ned Smarandachesemiquasi-near-ring. Some examples are constructed. We have posed some open problems.&nbsp

In this paper, we have introduced Smarandache quasigroups which are Smarandache non-associative structures. W.B.Kandasamy [2] has studied groupoid ring and loop ring. We have definedSmarandache quasigroup rings which are again non-associative structures having two binary operations.Substructures of quasigroup rings are also studied.