Abstract
The article describes a new concepts in fuzzy mathematics, we introduce fuzzy normed algebra over fuzzy field, Quasi -fuzzy norm, Quasi-p-fuzzy algebra over fuzzy field, Quasi- fuzzy algebra over fuzzy field, and quasi-p-fuzzy algebra over fuzzy field (S, F). We define convergent in fuzzy normed algebra over fuzzy field, Cauchy sequences in Quasi- fuzzy algebra over fuzzy field and open ball in it . Also, we prove every Quasi- normed algebra can be embedded in Quasi - Banach algebra X and an isometry L from X on to a sub algebra Y of X which is dense in X. The Quasi- algebra Ŷ is unique up to isometry, and an isometry L from X on to a sub algebra Y of X which is dense in X. The Quasi- algebra Ŷ is unique up to isometry.
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