×

zbMATH — the first resource for mathematics

Radicals of semigroups. (English) Zbl 0393.20047

MSC:
20M11 Radical theory for semigroups
20M25 Semigroup rings, multiplicative semigroups of rings
20M30 Representation of semigroups; actions of semigroups on sets
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Andrunakievič V.A.Radicals of associative rings, I, Matem. Sborn.44 (1958), 179–212 (Russian). · Zbl 0080.02602
[2] Andrunakievič, V.A.; Ju.M. Rjabuhin,Special modules and special radicals, Doklady Akad.Nauk SSSR147 (1962) 1274–1277 (Russian).
[3] —-,Modules and radicals, Doklady Akad. Nauk SSSR156 (1964), 991–994 (Russian).
[4] Arendt, B.D.,Semisimple bands, Doct. Diss., Univ. Iowa, 1967. · Zbl 0188.05502
[5] Arendt B,Semisimle bands, Trans.Amer.Math.Soc.143 (1919), 133–143.
[6] Arendt, B.,On semisimple commutative semigroups, Trans.Amer.Math.Soc.208 (1975), 341–351 · Zbl 0311.20045
[7] Baer, R.,Radical ideals, Amer. J. Math. 65 (1943), 537–568. · Zbl 0060.07104
[8] Burmistrovič, I.E.,Commutative bands of cancellative semigroups, Sibir. Matem. Zurn. 1965, 2842-304 (Russian).
[9] Clifford, A.H.,Radicals in semigroups, Semigroup Forum1 (1970), 103–128. · Zbl 0209.04801
[10] Clifford, A.H.; G.B. Preston,The algebraic theory of semigroups, Vols. I and II, Amer. Math.Soc., Providence, R.I., 1961 and 1917.
[11] Hoehnke, H.-J.,Uber das Radikal einer Primärkon-gruenz in einer kommutativen Halbgruppe, Bul. Inst. Politehn. Iasi10 (1964), 9–14 · Zbl 0147.00803
[12] —-,Uber das untere und obere Radikal einer Halbgruppe, Math. Z.89 (1965), 300–311. · Zbl 0201.36102
[13] —-,Eine Charakterisierung des Radikals kommutativer Halbgruppen, Arch. Math.16 (1965), 412–413. · Zbl 0156.26101
[14] —-,Einige neue Resultate über abstrakte Halbgruppen, Colloq. Math.14 (1964), 329–348. · Zbl 0196.29501
[15] —-,Structure of semigroups, Canad.J.Math.18 (1966), 449–491. · Zbl 0149.02402
[16] —-,Radikale in allgemeinen Algebren, Math. Nachr.32 (1966), 347–383. · Zbl 0149.02003
[17] —-,Das Brown –McCoy O-Radikal für Algebren und sceine Anwendung in der Theorie der Halbgruppen, Fund.Math.66 (1970), 155–175.
[18] Jacobson, N.,Structure of rings, Amer.Math.Soc., Providence, R.I., 1964. · Zbl 0117.03301
[19] Jordan,M.J.,H-semigroups and t-semisimple inverse H-semigroups, Trans.Amer.Math.Soc.163 (1972), 75–84. · Zbl 0229.20060
[20] —-,Periodic H-semigroups and t-semisimple periodic H-semigroups, Pacific J. Math.41 (1972), 437–446. · Zbl 0212.35901
[21] Krempa, J.,Logical connection between some open problems concerning nil-rings, Fund.Math.76 (1972), 121–130. · Zbl 0236.16004
[22] LaTorre, D.,Modular congruences and the Brown –McCoy radical for semigroups, Proc.Amer.Math.Soc.29 (1971), 427–433. · Zbl 0224.20060
[23] Monk, J.D.,Introduction to set theory, McGraw Hill, New York, N.Y., 1969. · Zbl 0200.00066
[24] Oehmke, R.H.,On maximal congruences and finite semisimple semigroups, Trans.Amer.Math.Soc.125 (1966), 223–237. · Zbl 0158.02101
[25] Petrich, M.,Introduction to semigroups, Merrill, Columbus, OH, 1973. · Zbl 0321.20037
[26] Roîz, E.N.,Radicals of semigroups, Candidate dies., Saratov Univ., 1973.(Russian).
[27] —-,On the compressive radical of semigroups, Matem.Sborn.92 (1973), 530–540 (Russian).
[28] —-,On the theory of radicals of semigroups, Studies in Algebra, Saratov3 (1973), 64–71.(Russian).
[29] —-,Strongly J-equiradical rings, Theory of Semi-groups and Its Applications, Saratov3 (1974), 85–89 (Russian).
[30] –,On the Jacobson and Baer radicals of rings and their multiplicative semigroups, Izv. Vyss. Učebn. Zaved. 1975, No.10, 71–79 (Russian).
[31] —-; B.M. Schein,The Brown –McCoy radical and the simple radical of semigroups, Uspehl Matem. Nauk28 (1973), No. 6, 215–216 (Russian).
[32] Schein, B.M.,A system of arioms for semigroups embeddable in generalized groups, Doklady Akad. Nauk SSSR134 (1960), 1030–1033 (Russian).
[33] Schein, B.M.,Embedding semigroups in generalized groups, Matem.Sborn.55 (1961), 379–400 (Russian).
[34] —-,On transitive representations of semigroups, Uspehl Matem. Nauk18 (1963), No.3, 215–222 (Russian). · Zbl 0126.04202
[35] —-,Representations of semigroups by means of binary relations, Matem.Sborn.60 (1963), 293–303 (Russian).
[36] —-,Representation of ordered semigroups, Matem.Sborn.65 (1964), 188–197 (Russian).
[37] —-,One-sided nilpotent semigroups, Uspehi matem. Nauk19 (1964), No.1, 187–197 (Russian).
[38] —-,On the theory of generalized groups and generalized grounds, Theory of Semigroups and Its Appl., Saratov1 (1965), 286–324 (Russian).
[39] –,On certain classes of semigroups of binary relations, Sibir.Matem.Zurn. 1965, 616–635 (Russian).
[40] —-,Homomorphisms and subdirect decompositions of semigroups, Pacific J. Math.17 (1966), 529–547. · Zbl 0197.01603
[41] –,On the theory of radicals of semigroups, Summaries of Talks, VIII-th All-Union Colloq.General Algebra, Riga, 1967, 131–132 (Russian).
[42] –,Representations of semigroups, Summaries of Talks, I-st All-Union Sympos.Theory of Semigroups, Sverdlovsk, 1969, 79–89.(Russian).
[43] –,Stationary subsets,stabilizers and transitive representations of semigroups, Dissertationes Math.77(1970). · Zbl 0219.20050
[44] —-,On semigroup radicals, Studien zur Algebra und ihre Anwend., Berlin1 (1976), 49–53.
[45] —-,Embedding semigroups in inverse semigroups, Algebra and Number Theory, Nalčik2 (1977), 147–163 (Russian).
[46] –,On semisimple bands, Semigroup Forum, to appear.
[47] —-;, A. Wiweger,How to divide by an empty set? Wiadomosci Mat.15 (1972), 13–15 (Polish).
[48] Seidel, H.,Über das Radikal einer Halbgruppe, Math. Nachr.29 (1965), 255–263. · Zbl 0128.25101
[49] Sierpiński, W.,Cardinal and ordinal numbers, PWN, Warszawa, 1965. · Zbl 0131.24801
[50] Skornjakov, L.A.,On radicals of {\(\Omega\)}-rings, Selected Problems in Algebra and Logic,-Novosibirsk, 1973, 283–299 (Russian).
[51] Slover, R.The radicals of semigroups, Trans.Amer. Math.Soc.204 (1975), 179–195. · Zbl 0308.20046
[52] Strecker, R.,Homomorphe Abbildungen auf Gruppen und das Radikal \(\overline {rad}\) S, Math. Nachr.62 (1974), 45–55. · Zbl 0291.20079
[53] Strecker, R.,Über das Radikal H-kommutativer Halbgruppen, Math.Nachr.68 (1975), 49–57. · Zbl 0333.20049
[54] —-,Uber das Radikal links-archimedischer Halbgruppen, Studien zur Algebra und ihre Anwend., Berlin, 1 (1976), 69–70.
[55] Thierrin, G.,Contribution à la théorie des anneaux et des demi-groupes, Comm.Math.-Helv.32 (1957), 93–112. · Zbl 0079.24902
[56] —-,Sur le radical corpoidal d’un anneau, Canad. J.Math.12 (1960), 101–106. · Zbl 0092.03801
[57] Tiščenko, A.V.,Special radicals in semigroups, Candidate dissertation, Moscow University, 1974(Russian).
[58] —-,Weakly special and special radicals in semigroups, Matem.Sborn.94 (1974), 551–566 (Russian). · Zbl 0325.20057
[59] —-,On the Brown –McCoy radical in semigroups, Math.Nachr.63 (1974), 401–414. · Zbl 0291.20078
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.