Leeson, J. J.; Butson, A. T. Equationally complete (m,n) rings. (English) Zbl 0461.16030 Algebra Univers. 11, 28-41 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 Documents MSC: 16Y60 Semirings 20N15 \(n\)-ary systems \((n\ge 3)\) 16P10 Finite rings and finite-dimensional associative algebras 16Dxx Modules, bimodules and ideals in associative algebras Keywords:equationally complete (m,n)-rings; (m,n)-ring; supersimple (m,n)ring; atomic variety of (m,n)-rings PDFBibTeX XMLCite \textit{J. J. Leeson} and \textit{A. T. Butson}, Algebra Univers. 11, 28--41 (1980; Zbl 0461.16030) Full Text: DOI References: [1] Birkhoff, G.,Lattice Theory, Amer. Math. Soc. Coll. Pub. Vol. XXV., 1967. · Zbl 0153.02501 [2] Clark, D. M., andP. H. Krauss,Para Primal Algebras, Algebra Universalis,6 (1976), 165–192. · Zbl 0368.08004 [3] Cohn, P. M.,Universal Algebra, Harper, New York, 1965. [4] Crombez, G.,On (n, m)-rings, Abh. Math. Sem. Univ. Hamburg,37 (1972), 180–199. · Zbl 0247.08001 [5] Kalicki, J. andD. Scott,Equational Completeness of Abstract Algebras, Indag. Math.17 (1955), 650–659. · Zbl 0073.24501 [6] Kaplansky, I.,Commutative Rings, Allyn & Bacon, Inc., Boston, 1970. · Zbl 0203.34601 [7] Leeson, J. J. andA. T. Butson,On the general theory of (m, n) rings, Algebra Universalis,11 (1980), 42–76. · Zbl 0461.16029 [8] Monk, J. D. andF. M. Sioson,On the general theory of m-groups, Fund. Math.,72 (1971), 233–244. · Zbl 0226.20079 [9] Neumann, H.,Varieties of Groups, Springer Verlag, New York, 1967. · Zbl 0149.26704 [10] Orr, G. F.,The lattice of varieties of semirings, doctoral Dissertation, Univ. of Miami, 1973. [11] Page, W. F.,The lattice of equational classes of m-semigroups, Doctoral Dissertation, Univ. of Miami, 1973. · Zbl 0287.08004 [12] Tarski, A.,Equationally complete rings and relation algebras, Indag. Math.,18 (1956), 39–46. · Zbl 0073.24603 [13] Taylor, W.,The Fine Spectrum of a Variety, Algebra Universalis,5 (1975), 263–303. · Zbl 0336.08004 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.