Some results on pseudo MV-algebras with square roots

On EMV-algebras with square roots

“…Recall that, in [DvZa3], we found some results about symmetric representing pseudo MV-algebras with square root with the additional condition u/2 ∈ C(G). The following lemma shows that the assumption u/2 ∈ C(G) is superfluous.…”

“…Otherwise, the only Boolean elements of M i are 0 and 1, so by Proposition 2.4(11)(b), r i (0) − ⊙ r i (0) − = 0 or r i (0) − ⊙ r i (0) − = 1. The equality r i (0) − ⊙ r i (0) − = 0 implies that r i (0) − ≤ r i (0) consequently, r i (0) − = r i (0) ([DvZa3, (4.1)]) which means r i is strict and so M i is symmetric by [DvZa3,Thm 5.6]. If r i (0) − ⊙ r i (0) − = 1, then r i (0) = 0.…”

“…In this paper, we continue with the study from [DvZa4], where we have studied square roots on pseudo MV-algebras. Square roots on pseudo MV-algebra were generalized from ones on MV-algebras in [DvZa3]. Motivation for studying square roots and strict square roots and their basic properties can be found in [DvZa3] together with the necessary notions and definitions.…”

“…Square roots on pseudo MV-algebra were generalized from ones on MV-algebras in [DvZa3]. Motivation for studying square roots and strict square roots and their basic properties can be found in [DvZa3] together with the necessary notions and definitions. In this part, sections, theorems, propositions, lemmas, examples, and equations are numbered in continuation of [DvZa4].…”

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In [DvZa3], we started the investigation of pseudo MV-algebras with square roots. In the present paper, the main aim is to continue to study the structure of pseudo MV-algebras with square roots focusing on their new characterizations.

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