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For a variety with weak existentially definable factor congruences, we characterize when the properties “→e→e is a central element” and “→e and →f are complementary central elements” are definable by (∀∧p=q)-formulas and by (∧p=q)-formulas.
In this paper, we introduce the concept of Birkhoff center of a c-semiring and provide some characterizations of this center. Finally, we prove that the Birkhoff center of a c-semiring forms a distributive lattice.
Elements of the exocenter of a generalized pseudoeffect algebra (GPEA) correspond to decompositions of the GPEA as a direct sum and thus the exocenter is a generalization to GPEAs of the center of a pseudoeffect algebra. The exocenter of a GPEA is shown to be a boolean algebra, and contains the central elements as a special subclass.