×
Kennison, John F.

Integral domain type representations in sheaves and other topoi. (English) Zbl 0331.18011

Math. Z. 151, 35-56 (1976).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0331.18011

Cited in 1 Review
Cited in 11 Documents

MSC:

18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
18C99 Categories and theories
06F25 Ordered rings, algebras, modules
54C40 Algebraic properties of function spaces in general topology
Cite Review PDF
Full Text: DOI EuDML

References:

[1] Appelgate, H., Tierney, M.: Categories with models. In: Seminar on Triples and Categorical Homology Theory. pp. 156-244. Lecture Notes in Mathematics 80. Berlin-Heidelberg-New York: Springer 1969 · Zbl 0188.28204
[2] Birkhoff, G.: Lattice Theory. Providence: American Mathematical Society, 1963 · Zbl 0122.02101
[3] Birkhoff, G., Pierce, R.S.: Lattice-ordered rings. Anais Acad. Brasil. Ci.28, 41-69 (1956) · Zbl 0070.26602
[4] Evans, H.: Various topics concerning Baer rings. Dissertation, Tulane University, New Orleans, 1972
[5] Eilenberg, S., Moore, J.C.: Adjoint Functors and Triples. Illinois J. Math.9, 381-398 (1965) · Zbl 0135.02103
[6] Fakir, S.: Monade idempotente associée à un monade. C. r. Acad. Sci., Paris270, 99-101 (1970) · Zbl 0287.18006
[7] Fuchs, L.: Partially ordered algebraic systems. Oxford: Pergamon Press, 1963 · Zbl 0137.02001
[8] Hofmann, K. H.: Representations of algebras by continuous sections. Bull. Amer. math. Soc.78, 291-373 (1972) · Zbl 0237.16018 · doi:10.1090/S0002-9904-1972-12899-4
[9] Keimel, K.: The representation of lattice-ordered groups and rings by sections in sheaves. In: Lectures on the Applications of Sheaves to Ring Theory (New Orleans 1970-1971) pp. 2-99. Lecture Notes in Mathematics 248. Berlin-Heidelberg-New York: Springer 1971
[10] Kennison, J., Gildenhuys, D.: Equational completion model induced triples and pro-objects. J. pure appl. Algebra,1, 317-346 (1971) · Zbl 0234.18006 · doi:10.1016/0022-4049(71)90001-6
[11] Kennison, J.: Triples and compact sheaf representations. J. pure appl. Algebra (to appear) · Zbl 0457.18011
[12] Lambek, J.: Localization and completion. J. pure appl. Algebra,2, 343-370 (1972) · Zbl 0281.16002 · doi:10.1016/0022-4049(72)90011-4
[13] Lambek, J., Rattray, B.: Localization and codensity triples. Commun. Algebra,1, 145-164 (1974) · Zbl 0281.18007 · doi:10.1080/00927877408548612
[14] MacLane, S.: Categories for the working mathematician, Berlin-Heidelberg-New York: Springer 1971 · Zbl 0705.18001
[15] Mislove, M.: The existence and structure ofIRR(x). Semigroup Forum4, 1-33 (1972) · Zbl 0292.20055 · doi:10.1007/BF02570766
[16] Mulvey, C.: Intuitionistic Algebra and Representations of Rings. Mem. Amer. math. Soc.148, 3-57 (1974) · Zbl 0274.18012
[17] Osius, G.: Logical and set theoretical tools in elementary topoi. In: Model Theory and Topoi. pp. 297-346. Lecture Notes in Mathematics 445. Berlin-Heidelberg-New York: Springer 1975 · Zbl 0348.18002
[18] Pierce, R. S.: Modules over commutative regular rings. Mem. Amer. math. Soc.,70 (1967) · Zbl 0152.02601
[19] Pierce, R. S.: Radicals in function rings. Duke Math. J.23, 253-261 (1956) · Zbl 0071.26002 · doi:10.1215/S0012-7094-56-02323-7
[20] Wolf, A.: Sheaf representations of arithmetical algebras. Mem. Amer. math. Soc.148, 87-93 (1974) · Zbl 0274.08009
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.