Right fully idempotent rings need not be left fully idempotent

Fully idempotent and coidempotent modules

In this paper, the notion of fully idempotent modules is defined and it is shown that this notion inherits most of the essential properties of the usual notion of von Neumann's regular rings. Furthermore, we introduce the dual notion of fully idempotent modules (that is, fully coidempotent modules) and investigate some properties of this class of modules.

fully idempotent and coidempotent modules

in this paper, the notion of fully idempotent modules is defined and it is shown that this notion inherits most of the essential properties of the usual notion of von neumann's regular rings. furthermore, we introduce the dual notion of fully idempotent modules (that is, fully coidempotent modules) and investigate some properties of this class of modules.

Non-idempotent left symmetric left distributive groupoids

Subdirectly irreducible non-idempotent groupoids satisfying x · xy = y and x · yz = xy · xz are studied.

Sheaves over Right Sided Idempotent Quantales

Idempotent Full Paraconsistent Negations are not Algebraizable

Using methods of abstract logic and the theory of valuation, we prove that there is no paraconsistent negation obeying the law of double negation and such that ¬(a ∧ ¬a) is a theorem which can be algebraized by a technique similar to the Tarski-Lindenbaum technique. 1 What are the features of a paraconsistent negation? Since paraconsistent logic was launched by da Costa in his seminal paper [4]...