Extending Homomorphisms of Dense Projective Subplanes by Continuity

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras

Subplanes of Order 3 in Hughes Planes

L. Puccio and M. J. de Resmini [5] showed that subplanes of order 3 exist in the Hughes plane of order 25. (We refer always to the ordinary Hughes planes; equivalently, all our nearfields are regular.) Computations of the second author [2] show that among the known projective planes of order 25 (including 99 planes up to isomorphism/duality), exactly four have subplanes of order 3. These four p...

$PI$-extending modules via nontrivial complex bundles and Abelian endomorphism rings

A module is said to be $PI$-extending provided that every projection invariant submodule is essential in a direct summand of the module. In this paper, we focus on direct summands and indecomposable decompositions of $PI$-extending modules. To this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper ...

Boundedness and Continuity of Fuzzy Linear Order-Homomorphisms on $I$-Topological\ Vector Spaces

In this paper, a new definition of bounded fuzzy linear orderhomomorphism on $I$-topological vector spaces is introduced. Thisdefinition differs from the definition of Fang [The continuity offuzzy linear order-homomorphism. J. Fuzzy Math. {bf5}textbf{(4)}(1997), 829--838]. We show that the ``boundedness"and `` boundedness on each layer" of fuzzy linear orderhomomorphisms do not imply each other...

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...