On Pierce Stalks of Semirings

G. Bredon, Sheaf Theory, McGraw-Hill, New York (1967). W. D. Burgess and W. Stephenson, “Pierce sheaves of non-commutative rings,” Commun. Algebra, 39, 512–526 (1976). W. D. Burgess and W. Stephenson, “An analogue of the Pierce sheaf for non-commutative rings,” Commun. Algebra, 6, No. 9, 863–886 (1978). W. D. Burgess and W. Stephenson, “Rings all of whose Pierce stalks are local,” Can. Math. Bull., 22, No. 2, 159–164 (1979). A. B. Carson, “Representation of regular rinds of finite index,” J. Algebra, 39, No. 2, 512–526 (1976). V. V. Chermnykh, “Sheaf representations of semirings,” Usp. Mat. Nauk, 48, No. 5, 185–186 (1993). V. V. Chermnykh, “Functional representations of semirings,” J. Math. Sci., 187, No. 2, 187–267 (2012). V. V. Chermnykh and R. V. Markov, “Pierce chains of semirings,” Vestn. Syktyvkar. Univ., Ser. 1, 16, 88–103 (2012). V. V. Chermnykh, E. M. Vechtomov, and A. V. Mikhalev, “Abelian regular positive semirings,” Tr. Semin. Petrovskogo, 20, 282–309 (1997). R. Cignoli, “The lattice of global sections of sheaves of chains over Boolean spaces,” Algebra Universalis, 8, No. 3, 357–373 (1978). S. D. Comer, “Representation by algebras of sections over Boolean spaces,” Pacific. Math., 38, 29–38 (1971). W. H. Cornish, “0-ideals, congruences and sheaf representations of distributive lattices,” Rev. Roum. Math. Pures Appl., 22, No. 8, 200–215 (1977). J. Dauns and K. H. Hofmann, “The representation of biregular rings by sheaves,” Math. Z., 91, No. 2, 103–123 (1966). G. Georgescu, “Pierce representations of distributive lattices,” Kobe J. Math., 10, No. 1, 1–11 (1993). K. Keimel, “The representation of lattice ordered groups and rings by sections in sheaves,” in: Lectures on the Applications of Sheaves to Ring Theory, Lect. Notes Math., Vol. 248, Springer, Berlin (1971), pp. 2–96. J. Lambek, Lectures on Rings and Modules, Waltham, Massachusets (1966) R. S. Pierce, “Modules over commutative regular rings,” Mem. Amer. Math. Soc., 70, 1–112 (1976). G. Szeto, “The sheaf representation of near-rings and its applications,” Commun. Algebra, 5, No. 7, 773–782 (1975). A. A. Tuganbaev, Ring Theory. Arithmetical Modules and Rings [in Russian], MCNMO, Moscow (2009). D. V. Tyukavkin, Pierce Sheaves for Rings with Involution [in Russian], Deposited at VINITI No. 3446-82 (1982).