This paper introduces a 'new' class of lattice ordered algebras. A lattice ordered algebra A will be called a pseudo f -algebra if xy = 0 for all x, y in A such that x ∧ y is a nilpotent element in A. Different aspects of archimedean pseudo f -algebras are considered in detail. Mainly their integral representations on spaces of continuous functions, as well as their connection with almost f -algebras and f -algebras. Various characterizations of order bounded multiplicators on pseudo f -algebras are given, where by a multiplicator on a pseudo f -algebra A we mean an operator T on A such that xT (y) = yT (x) for all x, y in A. In this regard, it will be focused on the relationship between multiplicators and orthomorphisms on pseudo f -algebras.

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À l'extrémité orientale du kef Dougga et en contrebas, les stèles votives figurées et inscrites en néopunique et en latin marquaient l'emplacement de vases cinéraires contenant des restes osseux offerts à Baal Hammon 1 , assimilé plus tard à Saturne 2 . Les vestiges de cette aire sacrée à ciel ouvert ont été localisés, entre 1891 et 1893, par Louis Carton et le lieutenant Denis au nord-ouest du sanctuaire reconstruit en 195, ou sousjacents à sa cour en 1927 par la direction des Antiquités, puis en 1954 par Claude Poinssot qui ont exhumé ces dépôts votifs 3 .

Abstract. In this paper we show that the range of norm one projection on Co(X) {X is a locally compact space) which satisfies the Seever's identity (T(fTg) = T(TfTg)) is isometrically isomorphic to Co(V) for some locally compact space Y. A short historical accountAn averaging operator was defined by Birkhoff [1] to be a linear operator T on a Banach algebra A satisfying the condition that:forall/, 5 €A Such operators were first used (implicitly) by Reynolds [7] in connection with the theory of turbulence. A number of characterizations of these operators in the special setting of contractive projections on Co (X) have appeared in the literature. Let T be a contractive projection on Co (X): T 2 = T, ||T|| = 1. Kelley [6] proved that if T is positive then T is averaging if and only if the range R(T) of T is a subalgebra of Co (X). After that, Seever [9] showed that the identity T(fTg) = T(TfTg), for all /, g e C Q (X)holds whenever T is positive. Some-how this result is a generalization of Kelley's theorem. For the sake of simpleness, an operator with the above identity will be called, in this space, a Seever operator. The result of Seever was obtained by Wulbert [12] in the compact case with a weaker condition on T. Indeed, T is a Seever operator as soon as R(T) has a weakly separating quotient. Later, Friedman and Russo [3] furnished an example in which they proved that the condition obtained by Wulbert is not necessary. However, they found an alternative condition which turns out to be necessary and sufficient for T to be a Seever operator. Different algebraic and lattice 1991 Mathematics Subject Classification: 47B48, 46E25.