• Journal of the Korean Mathematical Society
• /
• v.42 no.2
• /
• pp.291-304
• /
• 2005

We introduce a concept of Cauchy complete Csaszar frames and construct Cauchy completions of Csaszar frames using strict extensions of frames and show that the Cauchy completion gives rise to a coreflection in the categories CsFrm and UCsFrm.

• Communications of the Korean Mathematical Society
• /
• v.23 no.3
• /
• pp.453-459
• /
• 2008

We introduce a concept of continuous homomorphisms between Csaszar frames and show that the Cauchy completion in CsFrm gives rise to a coreflection in the category PCsFrm (resp. UCsFrm) consisting of proximal Csaszar frames and uniform continuous homomor-phisms (resp. uniform Csaszar frames and uniform continuous homomor-phisms).

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.5
• /
• pp.1067-1079
• /
• 2012

Let M be a right R-module, (S, ${\leq}$) a strictly totally ordered monoid which is also artinian and ${\omega}:S{\rightarrow}Aut(R)$ a monoid homomorphism, and let $[M^{S,{\leq}}]_{[[R^{S,{\leq}},{\omega}]]$ denote the generalized inverse polynomial module over the skew generalized power series ring [[$R^{S,{\leq}},{\omega}$]]. In this paper, we prove that $[M^{S,{\leq}}]_{[[R^{S,{\leq}},{\omega}]]$ has the same uniform dimension as its coefficient module $M_R$, and that if, in addition, R is a right perfect ring and S is a chain monoid, then $[M^{S,{\leq}}]_{[[R^{S,{\leq}},{\omega}]]$ has the same couniform dimension as its coefficient module $M_R$.