A new approach to a network of congruences on an inverse semigroup


Abstract in English

This paper enriches the list of known properties of congruence sequences starting from the universal relation and successively performing the operators lower $k$ and lower $t$. Two series of inverse semigroups, namely $ker{alpha_n}$-is-Clifford semigroups and $beta_n$-is-over-$E$-unitary semigroups, are investigated. Two congruences, namely $alpha_{n+2}$ and $beta_{n+2}$, are found to be the least $ker{alpha_n}$-is-Clifford and least $beta_n$-is-over-$E$-unitary congruences on $S$, respectively. A new system of implications is established for the quasivarieties of inverse semigroups induced by the min network.

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