Mazorchuk, Volodymyr Endomorphisms of \({\mathfrak B}_n\), \({\mathcal P}{\mathfrak B}_n\), and \({\mathfrak C}_n\). (English) Zbl 1008.20056 Commun. Algebra 30, No. 7, 3489-3513 (2002). Generalizing the concept of the symmetric group \(S_n\) of degree \(n\), the author considers the Brauer semigroup \({\mathfrak B}_n\) (its definition is too long for this review). The author generalizes \({\mathfrak B}_n\) to \({\mathcal P}{\mathfrak B}_n\). Another generalization of \({\mathfrak B}_n\) was given in [C. Xi, Compos. Math. 119, No. 1, 99-109 (1999; Zbl 0939.16006)]; although it considers algebras rather than semigroups, it is easy to define the corresponding semigroup \({\mathfrak C}_n\). The author finds endomorphisms of these semigroups and proves that all automorphisms of \({\mathfrak C}_n\) are inner. Reviewer: Boris M.Schein (Fayetteville) Cited in 27 Documents MSC: 20M20 Semigroups of transformations, relations, partitions, etc. 20M15 Mappings of semigroups Keywords:Brauer semigroups; endomorphisms; automorphisms Citations:Zbl 0939.16006 PDFBibTeX XMLCite \textit{V. Mazorchuk}, Commun. Algebra 30, No. 7, 3489--3513 (2002; Zbl 1008.20056) Full Text: DOI References: [1] Kargapolov M.I., 4 (1996) [2] Kerov S.V., (Russian) Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 164 (1987) [3] Mazorchuk V., Problems in Algebra 13 (1998) · Zbl 1098.17502 [4] Rotman J.J., 4 (1995) [5] DOI: 10.1006/jabr.1997.7132 · Zbl 0887.20033 · doi:10.1006/jabr.1997.7132 [6] DOI: 10.1090/S0002-9939-98-04764-9 · Zbl 0912.20047 · doi:10.1090/S0002-9939-98-04764-9 [7] DOI: 10.1080/00927879808826385 · Zbl 0918.20051 · doi:10.1080/00927879808826385 [8] Changchang Xi, Compositio Math. 119 pp 99– (1999) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.