@MISC{PUA2MSS1.MIZ,
  AUTHOR = {Bancerek, Grzegorz},
  TITLE = {Minimal Signature for Partial Algebra},
  ACKNOWLEDGEMENT = {I would like to thank Professor Andrzej Trybulec for suggesting me
the problem solved here.},
  SECTION1 = {Preliminary},
  SECTION2 = {Partitions},
  SECTION3 = {Relations Generated by Operations of Partial Algebra},
  SECTION4 = {Partitability},
  SECTION5 = {Signature Morphisms },
  SECTION6 = {Many Sorted Signature of Partial Algebra},
  DAY = {01},
  MONTH = {October},
  YEAR = {1995},
  ADDRESS1 = {Institute of Mathematics\\Polish Academy of Sciences},
  SUMMARY = {The concept of characterizing of partial algebras by many sorted signature
is introduced, i.e. we say that a signature $S$ characterizes a partial
algebra $A$ if there is an $S$-algebra whose sorts form a partition of
the carrier of algebra $A$ and operations are formed from operations
of $A$ by the partition.
The main result is that for any partial algebra
there is the minimal many sorted signature which
characterizes the algebra.
The minimality means that there are signature endomorphisms from
any signature which characterizes the algebra $A$ onto the minimal one.}}

