We introduce a symmetry property for unit-regular rings as follows: a∈ R is unit-regular if
and only if aR⊕(a− u) R= R (equivalently, Ra⊕ R (a− u)= R) for some unit u of R if and only …

A ring R is called left morphic if R/Ra≅ l (a) for every a∈ R. A left and right morphic ring is
called a morphic ring. If Mn (R) is morphic for all n≥ 1 then R is called a strongly morphic …

Let R be a unit-regular ring and let σ be an endomorphism of R such that σ (e)= e for all e2=
e∈ R and let n≥ 0. It is proved that every element of R [x; σ]/(xn+ 1) is equivalent to an …

In this dissertation, we study the relationships between the notions of a morphic element and
a morphic ring or module on one hand and reduced and regular rings or modules on the …

This paper contains new and known results on homomorphisms that are close to regular.
The main results are presented with proofs. All rings are assumed to be associative and with …

Regular Substructures of Hom Page 1 Appl Categor Struct (2008) 16:159–166 DOI 10.1007/s10485-007-9068-5
Regular Substructures of Hom Friedrich Kasch Received: 27 July 2006 / Accepted: 22 January …

For a ring R, call a class C of R-modules (pure-) mono-correct if for any M, N∈ C the
existence of (pure) monomorphisms M→ N and N→ M implies M≃ N. Extending results and …

The notion of $ R $-regular module is introduced. We will show that if $ M $ is a torsion-free
module over a commutative ring, then $ M $ is $ R $-regular module if and only if $ M $ is a …

We study the transfer of properties of some types of modules under identity preserving ring
homomorphisms. These studies seem to be overlooked in literature. We have picked a few …

I. Let~ o be a class of rings. It is natural to pose the question: for what rings R do the rings of
endomorphisms EndR (P) of all projective left modules RP belong to the class YF …