Robson, J. C. Well quasi-ordered sets and ideals in free semigroups and algebras. (English) Zbl 0404.16010 J. Algebra 55, 521-535 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 10 Documents MSC: 16Rxx Rings with polynomial identity 16S50 Endomorphism rings; matrix rings 16Dxx Modules, bimodules and ideals in associative algebras 16S10 Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) 15A24 Matrix equations and identities 20M12 Ideal theory for semigroups 20M05 Free semigroups, generators and relations, word problems 06A06 Partial orders, general Keywords:Polynomials Satisfied By a General Matrix over Noncommutative Ring; Ideals in a Free Associative Algebra; Free Semigroup; Finite Basis Property for Insertive Ideals PDFBibTeX XMLCite \textit{J. C. Robson}, J. Algebra 55, 521--535 (1978; Zbl 0404.16010) Full Text: DOI References: [1] Bergman, G. M.; Lewin, J., The semigroup of ideals of a fir is (usually) free, J. London Math. Soc., 11, 21-31 (1975) · Zbl 0275.16003 [2] Cohen, D. E., On the laws of a metabelian variety, J. Algebra, 5, 267-273 (1967) · Zbl 0157.34802 [3] Cohn, P. M., On subsemigroups of free semigroups, (Proc. Amer. Math. Soc., 13 (1962)), 347-351 · Zbl 0111.03801 [4] Gordon, R.; Robson, J. C., Krull Dimension, Mem. Amer. Math. Soc., 133 (1973) · Zbl 0269.16017 [5] Higman, G., Ordering by divisibility in abstract algebras, (Proc. London Math. Soc., 2 (1952)), 326-336 · Zbl 0047.03402 [6] Krause, G., On the Krull dimension of left Noetherian left Matlis rings, Math. Z., 118, 207-214 (1970) · Zbl 0194.06601 [7] Kruskal, J. B., The theory of well quasi-ordering: A frequently discovered concept, J. Combinatorial Theory A, 13, 297-305 (1972) · Zbl 0244.06002 [8] Rentschler, R.; Gabriel, P., Sur la dimension des anneaux et ensembles ordonnés, C. R. Acad. Sci. Paris Sér. A-B, 265, 712-715 (1967) · Zbl 0155.36201 [9] Robson, J. C., Polynomials satisfied by matrices, J. Algebra, 55, 509-520 (1978) · Zbl 0411.16016 [10] Sierpiński, W., Cardinal and Ordinal Numbers, Polska Akad. Nauk Monog. Matem. (1958) · Zbl 0083.26803 [11] Toulmin, G. H., Shuffling ordinals and transfinite dimension, (Proc. London Math. Soc., 4 (1954)), 177-195 · Zbl 0055.41406 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.