Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv
Theorem 1. If R is a morphic ring and aR ~ bR, cR ~ dR then
a) aR+cR ~ bR∩dR;
b) aR∩cR ~ bR+dR;
c) acR ~ (b:c)=(d:a);
d) tensor product of the principal ideals aR and bR is morphic to their interstion.
Theorem 2. If R is a morphic ring and aR ~ bR then a and b locally behave like usual integers.
Theorem 3. Morphic reduced ring is a von Neumann regular ring.
Theorem 4. If R is a commutative ring and I is its ideal then R/I is morphic iff for any element a+I of R/I there is some b+I in R/I such that (I:a)=bR+I, (I:b)=aR+I.