Leeson, J. J.; Butson, A. T. On the general theory of \((m,n)\) rings. (English) Zbl 0461.16029 Algebra Univers. 11, 42-76 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 5 Documents MSC: 16Y60 Semirings 16P10 Finite rings and finite-dimensional associative algebras 20N15 \(n\)-ary systems \((n\ge 3)\) Keywords:\(m\)-semigroups; \(m\)-groups; Post coset theorem; \((m,n)\)-rings; commutative \(m\)-groups; \((m,n)\)-division rings; \((m,n)\)-fields; lattices of congruences; finite \((m,n)\)-division rings Citations:Zbl 0025.01201 PDFBibTeX XMLCite \textit{J. J. Leeson} and \textit{A. T. Butson}, Algebra Univers. 11, 42--76 (1980; Zbl 0461.16029) Full Text: DOI References: [1] Crombez, G.,On (n, m)-rings, ABH. Math. Sem. Univ. Hamburg,37, 1972, pp 180–199. · Zbl 0247.08001 [2] Crombez, G., andJ. Timm,On (n, m)-quotient rings, ABH. Math. Sem. Univ. Hamburg,37, 1972, pp200–203. · Zbl 0247.08002 [3] Dörnte, W.,Untersuchen uber verallgemeinerten gruppenbegriff, Math. Zeit.,29, 1929, pp 1–19. · JFM 54.0152.01 [4] Monk, J. D. andF. M. Sioson,On the general theory of m-groups, Fund. Math.,72, 1971, pp 233–244. · Zbl 0226.20079 [5] Orr, G. F.,The lattice of varieties of semirings, Doctoral Dissertation, Univ. of Miami, 1973. [6] Page, W. F.,The lattice of equational classes of m-semigroups, Doctoral Dissertation, Univ. of Miami, 1973. · Zbl 0287.08004 [7] Post, E. L. Polyadic groups, Trans. Amer. Math. Soc.,48, 1940, pp 208–350. · JFM 66.0099.01 [8] Timm, J.,Kommutative n-gruppen, Doctoral Dissertation, Univ. of Hamburg, 1967. 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.