Retraction to: Semigroup Forum (2012) 85:369–380 DOI 10.1007/s00233-012-9423-1
I withdraw my paper “On right congruences of semigroups having no proper essential congruences” which appeared in Semigroup Forum 85 (2012), 369–380.
This paper is a somewhat expanded version of a rough note by my late supervisor Robert H. Oehmke. He sent over that manuscript to me in 1999, suggesting that I join in by completing the results and then we would publish a paper jointly. Due to unforeseen circumstances, I could not complete the paper until much later, in 2009. Unfortunately, Professor Oehmke had passed away in 2003 before I had an opportunity to show him my completed research. After searching for relative keywords in Google and finding nothing of any significant relevance, I submitted the expanded paper to Semigroup Forum in 2009.
I was shocked to learn now that Professor Oehmke himself had published the results from his rough notes in a paper entitled “On the distributivity of the lattice of right congruences of a semigroup”, Hadronic Journal 27 (2004), 458–472, submitted in 2003. Till now, I was unaware of this paper and of his decision, taken years after writing to me, to publish his own results based on the rough notes alone.
Clearly, a very large part of my paper coincides practically with large parts of Oehmke’s paper. Had I known about Oehmke’s paper, I would not have submitted mine, and therefore I withdraw my paper. I understand that I should have included a proper acknowledgement of the contribution from Robert H. Oehmke to my paper, giving him due credit for a large part of the results. I apologize that I did not do so. In addition, the main theorem in my paper contains errors that are not present in Professor Oehmke’s original notes, for which mistake I also apologize.
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The online version of the original article can be found under doi:10.1007/s00233-012-9423-1.
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Wu, Cy. Retraction Note: On right congruences of semigroups having no proper essential right congruences, Semigroup Forum (2012) 85:369–380. Semigroup Forum 87, 495–496 (2013). https://doi.org/10.1007/s00233-013-9502-y
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DOI: https://doi.org/10.1007/s00233-013-9502-y