Johnstone, P. T. Rings, fields, and spectra. (English) Zbl 0369.13019 J. Algebra 49, 238-260 (1977). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 15 Documents MSC: 13L05 Applications of logic to commutative algebra 13A15 Ideals and multiplicative ideal theory in commutative rings 14A05 Relevant commutative algebra 18D35 Structured objects in a category (MSC2010) 03C99 Model theory PDF BibTeX XML Cite \textit{P. T. Johnstone}, J. Algebra 49, 238--260 (1977; Zbl 0369.13019) Full Text: DOI OpenURL References: [1] Birkhoff, G, On the structure of abstract algebras, (), 433-454 · JFM 61.1026.07 [2] {\scJ. C. Cole}, The bicategory of topoi, and spectra, J. Pure Appl. Algebra, to appear. · Zbl 1401.18016 [3] Coste, M, Logique du premier ordre dans LES topos élémentaires, () [4] Coste, M, Une approche logique des théories définissables par limites projectives finies, () [5] Grothendieck, A; Verdier, J.L, Théorie des topos, (), (SGA 4, exposés I-VI) · Zbl 0256.18008 [6] Hakim, M, Topos annelés et schémas relatifs, () · Zbl 0246.14004 [7] Hochster, M, Prime ideal structure in commutative rings, Trans. amer. math. soc., 142, 43-60, (1969) · Zbl 0184.29401 [8] Johnstone, P.T, Internal categories and classification theorems, (), 103-113 · Zbl 0352.18010 [9] Johnstone, P.T, Topos theory, (1977), Academic Press London · Zbl 0368.18001 [10] {\scP. T. Johnstone and G. C. Wraith}, Algebraic theories in toposes, to appear. · Zbl 0392.18006 [11] Keane, O, Abstract Horn theories, (), 15-50 [12] Kennison, J.F, Integral domain type representations in sheaves and other topoi, Math. Z., 151, 35-56, (1976) · Zbl 0331.18011 [13] Kock, A, Universal projective geometry via topos theory, J. pure appl. algebra, 9, 1-24, (1976) · Zbl 0375.02016 [14] Labella, A, Costruzione del monoide dei quozienti in un topos elementare, Rend. mat. e appl. (VI), 7, 151-168, (1974) · Zbl 0352.18001 [15] Lawvere, F.W, Functorial semantics of algebraic theories, (), 869-872 · Zbl 0119.25901 [16] () [17] Lesaffre, B, Structures algébriques dans LES topos élémentaires, C. R. acad. sci. Paris Sér. A, 277, 663-666, (1973) · Zbl 0364.18006 [18] Mulvey, C.J, Intuitionistic algebra and representations of rings, Mem. amer. math. soc., 148, 3-57, (1974) · Zbl 0274.18012 [19] Osius, G, Logical and set-theoretical tools in elementary topoi, (), 297-346 [20] Osius, G, A note on Kripke-joyal semantics for the internal language of topoi, (), 349-354 [21] Pierce, R.S, Modules over commutative regular rings, Mem. amer. math. soc., 70, (1967) · Zbl 0152.02601 [22] Reyes, G.E, From sheaves to logic, (), 143-204 [23] Tierney, M, On the spectrum of a ringed topos, (), 189-210 [24] Tierney, M, Forcing topologies and classifying topoi, (), 211-219 · Zbl 0356.18012 [25] Volger, H, Completeness theorem for logical categories, (), 51-86 [26] Willard, S, General topology, (1970), Addison-Wesley Reading, Mass · Zbl 0205.26601 [27] Wraith, G.C, Lectures on elementary topoi, (), 114-206 · Zbl 0323.18005 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.