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A principal advantage of this abstract setting is that a vast body of existing theory becomes accessible for solving discrete tomography problems. We provide proofs of several new results on the structure of dependencies between projections, including a discrete analogon of the well-known Helgason\u2013Ludwig consistency conditions from continuous tomography.<\/jats:p>","DOI":"10.1137\/090766693","type":"journal-article","created":{"date-parts":[[2010,9,7]],"date-time":"2010-09-07T18:10:25Z","timestamp":1283883025000},"page":"1056-1079","source":"Crossref","is-referenced-by-count":3,"title":["An Algebraic Framework for Discrete Tomography: Revealing the Structure of Dependencies"],"prefix":"10.1137","volume":"24","author":[{"given":"Arjen","family":"Stolk","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"K. Joost","family":"Batenburg","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,9,7]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/040617443"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnt.2006.07.001"},{"key":"R3","unstructured":"M. F. Atiyah and I. G. Macdonald,\n                      Introduction to Commutative Algebra\n                      , Addison-Wesley, Reading, MA, London, Don Mills, ON, 1969."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1107\/S0108767306030091"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(94)00293-2"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01112819"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"M. S. Bazaraa, H. D. Sherali, and C. M. Shetty,\n                      Nonlinear Programming. 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