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The spectrum of a ring as a partially ordered set. (English) Zbl 0266.13010


MSC:

13C05 Structure, classification theorems for modules and ideals in commutative rings
06A06 Partial orders, general
13A15 Ideals and multiplicative ideal theory in commutative rings
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References:

[1] Cohn, P. M., Universal Algebra (1965), Harper and Row: Harper and Row New York · Zbl 0141.01002
[2] Gilmer, R. W., Multiplicative Ideal Theory, (Queen’s Papers, Lecture Notes No. 12 (1968), Queen’s University: Queen’s University Kingston, Ontario) · Zbl 0248.13001
[3] Gilmer, R. W.; Ohm, J., Integral domains with quotient overrings, Math. Ann., 153, 97-103 (1964) · Zbl 0128.26004
[4] Gilmer, R. W.; Ohm, J., Primary ideals and valuation ideals, Trans. Amer. Math. Soc., 117, 235-250 (1965) · Zbl 0133.29203
[5] Hochster, M., Prime ideal structure in commutative rings, Trans. Amer. Math. Soc., 142, 43-60 (1969) · Zbl 0184.29401
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[7] Kaplansky, I., Commutative Rings (1970), Allyn and Bacon: Allyn and Bacon Boston · Zbl 0203.34601
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[9] Krull, W., Beiträge zur Arithmetik kommutativer Integritätsbereiche, Math. Z., 41, 545-577 (1936) · JFM 62.1105.01
[10] Nagata, M., Local Rings (1962), Interscience: Interscience New York · Zbl 0123.03402
[11] Ohm, J., Semi-valuations and groups of divisibility, Can. J. Math., 21, 576-591 (1969) · Zbl 0177.06501
[12] J. Ohm and R. L. Pendleton; J. Ohm and R. L. Pendleton · Zbl 0172.32201
[13] Zariski, O.; Samuel, P., (Commutative Algebra, Vol. 1 (1958), Van Nostrand: Van Nostrand New York) · Zbl 0112.02902
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