The center of a \(\mathrm d_0\)-algebra. (English) Zbl 1473.06025
Summary: We define the center \(C(A)\) of a \(\mathrm d_0\)-algebra A as a set of self-mappings on \(A\). The center can be regarded as the set of all possible \(\mathrm d_0\)-subdirect factors of \(A\) which are subalgebras of \(A\). we show that \(C(A)\) is always a Boolean algebra. we also show that \(C(A)\) admits an embedding in the power \(A^\kappa\), where \(\kappa\) is the cofinality of \(A\). In case \(\kappa=1\) (i.e. \(A\) is a D-lattice) we reobtain the well-known fact that \(C(A)\) is a subalgebra of \(A\).
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