Using t-norm T, we introduce the notion of t-level subalgebra, and some related properties are investigated.

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Using a t-norm T, we introduce the notion of (imaginable) T-fuzzy subalgebras, (imaginable) T-fuzzy deductive systems and (imaginable) T-fuzzy ideals, and obtain some related results. We give relations between an imaginable T-fuzzy subalgebra and an imaginable fuzzy deductive system.

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In this work we provide a counterexample for Schur’s Theorem on triangular matrices on infinite dimensional spaces. Moreover, the counterexample provided is a compact quasinilpotent operator. Indeed, the result neither depends on the index of the chosen basis for the matrix representations nor on the upper-lower choice for the triangular matrix. As a consequence, we see the optimality of a result by Halmos on matrix representations of operators. Namely, Halmos proved that each operator can be represented by a matrix with finite columns. Finally, we ‘answer’ a philosophical question posed by J. B. Conway in [1, p.213].

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In this manuscript, at first we have given some theorems about nonisomorphic quasi union hyper K-algebra. Then we proceed with the study of classification quasi union hyper K-algebra of order less than or equal to 5. At the end, we give a conjecture about number of non-isomorphic quasi union hyper K-algebra of order n.

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All locally C^∗-structures on a commutative complex algebra have the same bound structure. It is also shown that a Mackey complete C^∗-convex algebra is semisimple.

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We investigate a simple notion of reduction for Reg11lar sets. We call this Moore reduction because the transformations use Moore machines. We show that under this reduction the Regular sets form a bi-hierarchy with complete sets.

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