ENDOMORPHISM RINGS AND FORMAL MATRIX RINGS OF PSEUDO-PROJECTIVE MODULES
Abstract
A module M is called pseudo-projective if every epimorphism from M to each quotient module of M can be lifted to an
endomorphism of M. In this paper, we study some properties of pseudoprojective modules and their endomorphism rings. It show that if M
is a self-cogenerator pseudo-projective module with finite hollow dimension, End(M) is a semilocal ring and every maximal right ideal of
End(M) has of the form {s ∈ End(M)| Im(s) + Ker(h) ̸= M} for some
endomorphism h of M with h(M) hollow. Moreover, it shows that
a pseudo-projective R-module M is an SSP-module if and only if the
product of any two regular elements of End(M) is a regular element.
Finally we investigate the pseudo-projectivity of modules over a formal
triangular matrix ring.
endomorphism of M. In this paper, we study some properties of pseudoprojective modules and their endomorphism rings. It show that if M
is a self-cogenerator pseudo-projective module with finite hollow dimension, End(M) is a semilocal ring and every maximal right ideal of
End(M) has of the form {s ∈ End(M)| Im(s) + Ker(h) ̸= M} for some
endomorphism h of M with h(M) hollow. Moreover, it shows that
a pseudo-projective R-module M is an SSP-module if and only if the
product of any two regular elements of End(M) is a regular element.
Finally we investigate the pseudo-projectivity of modules over a formal
triangular matrix ring.
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