On EMV-algebras with square roots

Square Roots in Banach Algebras

A complex number which is not a nonpositive real number has a unique square root in the right half-plane. In this paper, we obtain an extension of this observation to general (complex) Banach algebras. Since the elements we study are regular, and have logarithms, the existence of square roots is not at stake. Even the existence of roots having the desired spectral properties is evident. The uni...

On group Elements Having Square Roots

The Loomis–Sikorski Theorem for EMV -algebras

Recently, in [DvZa], we have introduced EMV -algebras which resemble MV -algebras but the top element is not guaranteed for them. For σ-complete EMV -algebras, we prove an analogue of the Loomis–Sikorski Theorem showing that every σ-complete EMV -algebra is a σ-homomorphic image of an EMV -tribe of fuzzy sets where all algebraic operations are defined by points. To prove it, some topological pr...

On the denesting of nested square roots

We present the basic theory of denesting nested square roots, from an elementary point of view, suitable for lower-level coursework. Necessary and sufficient conditions are given for direct denesting, where the nested expression is rewritten as a sum of square roots of rational numbers, and for indirect denesting, where the nested expression is rewritten as a sum of fourth-order roots of ration...

On square roots and norms of matrices with symmetry

The present work concerns the algebra of semi-magic square matrices. These can be decomposed into matrices of specific rotational symmetry types, where the square of a matrix of pure type always has a particular type. We examine the converse problem of categorising the square roots of such matrices, observing that roots of either type occur, but only one type is generated by the functional calc...