Let S be a foundation semigroup with identity and Ma(S) be its semigroup algebra. In this paper, we give necessary and su cient conditions for the existence of a bounded approxi-mate identity in CLOSED codimension one IDEALS of semigroup algebra Ma(S) of a locally compact topological foundation semigroup with identity.

Let S be a locally compact foundation semigroup with identity and ( ) be its semigroup algebra. Let X be a weak*-CLOSED left translation invariant subspace of ( ) In this paper, we prove that X is invariantly complemented in ( ) if and only if the left ideal of ( ) has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenable if and only if every complemented weak*-CLOSED left translation invariant subspace of ( ( )) is invariantly complemented in ( ( )).

In this paper, we study a generalization of z-IDEALS in the ring C (X) of continuous real valued functions on a completely regular Hausdorff space X. The notion of a weak ideal and naturally a weak z-ideal and a prime weak ideal are introduced and it turns out that they behave such as z -IDEALS in C (X).

Background and Aim: Different surgical techniques have been proposed for crown exposure among patients under orthodontic treatment. The aim of this study was to investigate periodontal indices in CLOSED flap operation technique used for impacted teeth crown exposure.Materials and Methods: In this descriptive study (2001-2003) 20 patients (15 females and 5 males), age ranging from 15 to 20 years, were participated. Following the performance of CLOSED flap operation technique, in 12 patients impacted canine and central incisors were exposed and treated orthodontically. Periodontal parameters including sulcular depth, width of keratinized gingiva and attachment loss were recorded. Results: The mean of gingival sulcus depth was 1.50±0.43, the means of keratinized gingival in central incisors and canines were 3.07±0.53 and 2.30±0.42, respectively. In one patient, attachment loss was reported.Conclusion: Considering the optimal sulcular depth and keratinized gingiva, the CLOSED flap operation technique seems suitable.

In this paper, we introduce the notion of hybrid bi-IDEALS in semigroups and investigate some of their important properties. We also give various equivalent conditions for a semigroup to be regular and hybrid structures to be hybrid bi-IDEALS of S.