Let k be a commutative ring and A and B be k-algebras and [alpha] is a unital partial action of a finite group G on A.
Actually, there are several equivalent conditions to say that A is a partial Galois extension of B (see [36, Theorem 4.1]).
Note that in the case of non-unital partial actions we cannot define the right A module structure on C.
In fact, It is shown in  that the classical results of HopfGalois theory and its relation to Morita theory are still valid in the context of partial actions.
The turning point in the theory was given in reference , in which coring techniques were strongly used to extend the notion of partial actions to the Hopf algebraic context.
In past, Preshaw et al9 said that wearing removable partial dentures although do increase the chance of periodontitis, they do overall improve the nutritional status of the individual and also play a role in improving the overall quality of life in the patients.
To oppose this, a review of extensive literature done by Petridis and Hampton10, showed that wearing removable partial denture does not cause any detrimental periodontal reactions, provided that pre-prosthetic periodontal health has been established and also oral health should be maintained via meticulous oral hygiene.
One of the important causes of failure of partial denture is that the teeth supporting the denture are lost in later years.
The current study was done to assess the periodontal status of natural teeth in contact with the removable partial denture to find out how the use of removable partial dentures affect health of adjacent teeth .Gingival, Plaque and Calculus index was measured in abutment teeth to assess their health.
Non-probabaility convenience sampling technique was used to select the sample In this follow-up study a total of 500 patients were examined from June 2016 to December 2016.Out of those 500 patients 200 patients were identified who were treated with removable partial denture and were having 0 score for gingival, plaque and calculus index.
Word [u.sub.[??]] = ba[??]ab[??]is the companion of the partial word.
The following rules are useful for computing with partial words:
Let u, v, x, y be partial words such that ux [up arrow] vy.
(i) If [absolute value of u] [greater than or equal to] [absolute value of v], then there exist partial words w, z such that u = wz, v [up arrow] w, and y [up arrow] zx.
(ii) If [absolute value of u] [less than or equal to] [absolute value of v], then there exist partial words w, z such that b = wz, v [up arrow] w, and x [up arrow] zy.