Approximate Regular Modules

GF-Regular Modules

We introduced and studied GF-regular modules as a generalization of π-regular rings to modules as well as regular modules (in the sense of Fieldhouse). An R-moduleM is called GF-regular if for each x ∈ M and r ∈ R, there exist t ∈ R and a positive integer n such that rntrnx = rx. The notion of G-pure submodules was introduced to generalize pure submodules and proved that an RmoduleM isGF-regula...

On Regular Modules

Several characterizations are given of (Zelmanowitz) regular modules among the torsionless modules, the locally projective modules, the nonsingular modules, and modules where certain submodules are pure. Along the way, a version of the unimodular row lemma for torsionless modules is given, and it is shown that a regular ring is left self-injective if and only if every nonsingular left module is...

Projective maximal submodules of extending regular modules

We show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. Hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. As aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. This generalizes and simplifies a result of  Dung and   Smith. As another consequen...

Approximate Regular Expression

Approximate Regular Expression Pattern

Given a sequence A of length M and a regular expression R of length P, an approximate regular expression pattern matching algorithm computes the score of the optimal alignment between A and one of the sequences B exactly matched by R. An alignment between sequences A = a 1 a 2 : : :a M and B = b 1 b 2 : : :b N is a list of ordered pairs, <(i 1 ; j 1); (i 2 ; j 2); : : :(i t ; j t)> such that i ...