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Regular congruences on an E-inversive semigroup

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Abstract

A semigroup S is called E-inversive if for any a∈S there exists x∈S such that ax∈E(S). In this paper, the regular congruences on an E-inversive semigroup are investigated. It is proved that each regular congruence ρ on an E-inversive semigroup S is uniquely determined by the pair (ker ρ,tr ρ) and an abstract characterization of regular congruence ρ by means of the pair (ker ρ,tr ρ) (called regular congruence pair) is given. Also it is shown that each regular congruence on S is uniquely determined by its kernel normal system and a description of the regular congruences on S in terms of their kernel normal systems is given.

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Authors and Affiliations

  1. Department of Mathematics, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Yanfeng Luo, Xingkui Fan & Xiaoling Li

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  1. Yanfeng Luo
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  2. Xingkui Fan
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  3. Xiaoling Li
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Correspondence to Yanfeng Luo.

Additional information

Communicated by Francis J. Pastijn

This research was partially supported by the EYTP of MOE of China, the National Natural Science Foundation of China (No. 10571077) and the Natural Science Foundation of Gansu Province (3ZS052-A25-017).

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Luo, Y., Fan, X. & Li, X. Regular congruences on an E-inversive semigroup. Semigroup Forum 76, 107–123 (2008). https://doi.org/10.1007/s00233-007-9015-7

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  • DOI: https://doi.org/10.1007/s00233-007-9015-7

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