Abstract
We investigate ideals of a commutative ring that are an irredundant union of principal ideals. Special attention is paid to prime ideals that are a finite union of principal ideals.
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Anderson, D.D.: Some finiteness conditions on a commutative ring. Houst. J. Math. 4, 289–299 (1978)
Anderson, D.D., Chun, S.: Irreducible elements in commutative rings with zero divisors. Houst. J. Math. 37, 741–744 (2011)
Anderson, D.D., Chun, S.: A class of atomic rings. Commun. Algebra (to appear)
Anderson, D.D., Markanda, R.: Unique factorization rings with zero divisors. Houst. J. Math. 11, 15–30 (1985)
Anderson, D.D., Valdes-Leon, S.: Factorization in commutative rings with zero divisors. Rocky Mt. J. Math. 26, 439–480 (1996)
Anderson, D.D., Winders, M.: Idealization of a module. J. Commut. Algebra 1, 3–56 (2009)
Gilmer, R.: Multiplicative Ideal Theory. Queen’s Papers in Pure and Appl. Math., vol. 90. Queen’s University, Kingston (1992)
Grams, A.: Atomic rings and the ascending chain condition for principal ideals. Proc. Camb. Philos. Soc. 75, 321–329 (1974)
Kaplansky, I.: Commutative Rings. Polygonal Press, Washington (1994)
McCoy, N.: A note on finite unions of ideals and subgroups. Proc. Am. Math. Soc. 8, 633–637 (1957)
Quartararo, P. Jr., Butts, H.S.: Finite unions of ideals and modules. Proc. Am. Math. Soc. 52, 91–96 (1975)
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Anderson, D.D., Chun, S. Ideals that are an irredundant union of principal ideals. Rend. Circ. Mat. Palermo 61, 133–141 (2012). https://doi.org/10.1007/s12215-012-0081-7
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DOI: https://doi.org/10.1007/s12215-012-0081-7