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Communications in Algebra Volume 51, 2023 - Issue 7
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Research Articles

Ascending chain conditions on right ideals of semigroups

Craig MillerDepartment of Mathematics, University of York, York, UKCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-5731-0953
ORCID Icon
Pages 2995-3014 | Received 21 Jul 2022, Accepted 20 Jan 2023, Published online: 13 Feb 2023

References

  • Aubert, K. (1953). On the ideal theory of commutative semi-groups. Math. Scand. 1:39–54. DOI: 10.7146/math.scand.a-10363.
  • Book, R., Otto, F. (1993). String Rewriting Systems. New York: Springer-Verlag.
  • Clifford, A. (1948). Semigroups containing minimal ideals. Am. J. Math. 70:521–526. DOI: 10.2307/2372195.
  • Clifford, A., Preston, G. (1961). The Algebraic Theory of Semigroups: Volume 1. Providence, RI: American Mathematical Society.
  • Clifford, A., Preston, G. (1967). The Algebraic Theory of Semigroups: Volume 2. Providence, RI: American Mathematical Society.
  • Davvaz, B., Nazemian, Z. (2020). Chain conditions on commutative monoids. Semigroup Forum 100:732–742. DOI: 10.1007/s00233-019-10032-1.
  • Good, R., Hughes, D. (1952). Associated groups for a semigroup. Bull. Am. Math. Soc., 58:624–625.
  • Hotzel, E. (1975). On semigroups with maximal conditions. Semigroup Forum 11:337–362. DOI: 10.1007/BF02195275.
  • Jespers, E., Okniński, J. (1999). Noetherian semigroup algebras. J. Algebra 218:543–564. DOI: 10.1006/jabr.1999.7870.
  • Kilp, M., Knauer, U., Mikhalev, A. (2000). Monoids, Acts and Categories. Berlin: Walter de Gruyter.
  • Kozhukhov, I. (1980). On semigroups with minimal or maximal condition on left congruences. Semigroup Forum 21:337–350. DOI: 10.1007/BF02572558.
  • Kozhukhov, I. (2003). Semigroups with certain conditions on congruences. J. Math. Sci. 114:1119–1126. DOI: 10.1023/A:1021921518767.
  • Lang, S. (2002). Algebra. New York: Springer-Verlag.
  • Lajos, S. (1963). Notes on (m, n)-ideals. I. Proc. Jpn. Acad. 39:419–421.
  • Liu, Z. (2004). The ascending chain condition for principal ideals of rings of generalized power series. Commun. Algebra 32:3305–3314.
  • Mazurek, R., Ziembowski, M. (2009). The ascending chain condition for principal left or right ideals of skew generalized power series rings. J. Algebra 322:983–994.
  • Miller, C., Ruškuc, N. (2020). Right noetherian semigroups. Int. J. Algebra Comput. 30:13–48.
  • Miller, C. (2021). Semigroups whose right ideals are finitely generated. Proc. Edinburgh Math. Soc. 64:848–883.
  • Noether, E. (1921). Idealtheorie in Ringbereichen. Math. Ann. 83:24–66.
  • Satyanarayana, M. (1972). Semigroups with ascending chain condition. J. London Math. Soc. 2–5:11–14.
  • Stopar, N. (2012). Ascending chain conditions on principal left and right ideals for semidirect products of semigroups. Semigroup Forum 85:322–336.

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