122
Views
12
CrossRef citations to date
0
Altmetric
Original Articles

Partial Maps with Domain and Range: Extending Schein's Representation

&
Pages 2845-2870 | Received 20 Mar 2007, Published online: 22 Jul 2009

REFERENCES

  • Batbedat , A. ( 1981 ). γ-Demi-Groups, Demi-Modules, Produit Demi-Directs . Semigroups, Proceedings, Oberwolfalch, Germany 1978, Lecture Notes in Mathematics 855 . Springer-Verlag , pp. 1 – 18 .
  • Bredihin , D. A. ( 1976 ). Inverse semigroups of local automorphisms of universal algebras . Sibirsk. Mat. Ž. 17 : 499 – 507, 715 [Russian; English translation in Siberian Math. J. 17(3):386–392] .
  • Bredihin D. A. ( 1977 ). An abstract characterization of some classes of algebras of binary relations . Algebra and Number Theory 2 : 3 – 19 . Kabardino-Balkarsk. Gos. Univ., Nalchik [Russian] .
  • Cockett , J. R. B. , Lack , S. ( 2002 ). Restriction categories I: Categories of partial maps . Theoret. Comput. Sci. 270 : 223 – 259 .
  • Desharnais , J. , Möller , B. , Struth , G. (2006). Kleene algebra with domain. ACM Trans. Comput. Log. 7:798–833.
  • Dudek , W. , Trokhimenko , V. S. ( 2002 ). Functional Menger 𝒫-algebras . Comm. Algebra 30 : 5921 – 5931 .
  • Fountain , J. ( 1979 ). Adequate semigroups . Proc. Edinburgh Math. Soc. 22 : 113 – 125 .
  • Fountain , J. ( 1991 ). Free Right Type A semigroups . Glasgow Math. J. 33 : 135 – 148 .
  • Garvac'kiĭ , V. S. ( 1971 ). ∩-semigroups of transformations . Teor. Polugrupp Prilozh. 2 : 2 – 13 [Russian] .
  • Gomes , G. M. S. , Gould , V. ( 1999 ). Proper weakly left ample semigroups . Internat. J. Algebra Comput. 9 : 721 – 739 .
  • Gould , V. , Kambites , M. ( 2005 ). Faithful functors from cancellative categories to cancellative monoids with an application to abundant semigroups . Internat. J. Algebra Comput. 15 : 683 – 698 .
  • Hirsch , R. , Hodkinson , I. ( 2001 ). Representability is not decidable for finite relation algebras . Trans. Amer. Math. Soc. 353 : 1403 – 1425 .
  • Jackson M. , Stokes , T. ( 2001 ). An invitation to C-semigroups . Semigroup Forum 62 : 279 – 310 .
  • Jackson M. , Stokes , T. ( 2003 ). Agreeable semigroups . J. Algebra 266 : 393 – 417 .
  • Jackson M. , Stokes , T. ( 2006a ). Identities in the algebra of partial maps . Internat. J. Algebra Comput. 16 : 1131 – 1159 .
  • Jackson M. , Stokes , T. ( 2006b ). The abstract algebra of order preserving partial maps, manuscript .
  • Jackson M. , Stokes , T. ( 2007 ). Algebras of partial maps, to appear. In: Proceedings of the Special Interest Meeting on Semigroups and Related Mathematics, University of Sydney 2005 .
  • Kelarev , A. , Stokes , T. ( 1999 ). Interior algebras and varieties . J. Algebra 221 : 50 – 59 .
  • Kozen , D. ( 2000 ). On Hoare logic and Kleene algebra with tests . ACM Trans. Comput. Log. 1 : 60 – 76 .
  • Lawson , M. ( 1991 ). Semigroups and ordered categories. I. The reduced case . J. Algebra 141 : 422 – 462 .
  • Leech , J. ( 1995 ). Inverse monoids with a natural semilattice ordering . Proc. London Math. Soc. 70 : 146 – 182 .
  • Manes , E. ( 2006 ). Guarded and banded semigroups . Semigroup Forum 72 : 94 – 120 .
  • Menger , K. ( 1959 ). An axiomatic theory of functions and fluents . Studies Logic Found. Math.,Axiomatic Method pp. 454 – 473 .
  • Schein , B. M. ( 1964 ). The representation of ordered semigroups . Mat. Sb. (N.S.) 65 ( 107 ): 188 – 197 [Russian] .
  • Schein , B. M. ( 1970a ). Restrictively multiplicative algebras of transformations . Izv. Vysš. Učebn. Zaved. Matematika 4 ( 95 ): 91 – 102 [Russian] .
  • Schein , B. M. ( 1970b ). Relation algebras and function semigroups . Semigroup Forum 1 : 1 – 62 .
  • Schein , B. M. ( 1979 ). Lectures on semigroups of transformations . Amer. Math. Soc. Translat. 113 ( 2 ): 123 – 181 .
  • Schein , B. M. ( 1992 ). Difference semigroups . Comm. Algebra 20 : 2153 – 2169 .
  • Schein , B. M. , Trokhimenko , V. S. ( 1979 ). Algebras of multiplace functions . Semigroup Forum 17 : 1 – 64 .
  • Schweizer , B. , Sklar , A. ( 1960 ). The algebra of functions . Math. Ann. 139 : 366 – 382 .
  • Schweizer , B. , Sklar , A. ( 1961 ). The algebra of functions II . Math. Ann. 143 : 440 – 447 .
  • Schweizer , B. , Sklar , A. ( 1965 ). The algebra of functions III . Math. Ann. 161 : 171 – 196 .
  • Schweizer , B. , Sklar , A. ( 1967 ). Function systems . Math. Ann. 172 : 1 – 16 .
  • Trokhimenko , V. S. ( 1973 ). Menger's function systems . Izv. Vys[sbreve]. Učebn. Zaved. Matematika 11 ( 138 ): 71 – 78 [Russian] .
  • Communicated by V. Gould.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.