Every Filter is Homeomorphic to Its Square

Every cockroach is beautiful to its mother.

cockroaches is not easy to document, given the precarious hygienic conditions of some of the habitats where they live. In fact, asthma is the only disease consistently associated with exposure to cockroaches [4–6] . Curiously enough, cockroaches have no lungs (they breathe through lateral spiracles in the body) [1] , but inhalation of cockroach materials by humans may trigger IgE antibody respo...

2 ' Is Homeomorphic to the Hilbert Cube

When every $P$-flat ideal is flat

In this paper‎, ‎we study the class of rings in which every $P$-flat‎ ‎ideal is flat and which will be called $PFF$-rings‎. ‎In particular‎, ‎Von Neumann regular rings‎, ‎hereditary rings‎, ‎semi-hereditary ring‎, ‎PID and arithmetical rings are examples of $PFF$-rings‎. ‎In the context domain‎, ‎this notion coincide with‎ ‎Pr"{u}fer domain‎. ‎We provide necessary and sufficient conditions for‎...

When Every Square Inch Counts TM

A square matrix is congruent to its transpose

For any matrix X let X′ denote its transpose. We show that if A is an n by n matrix over a field K , then A and A′ are congruent over K , i.e., P ′AP =A′ for some P ∈ GLn(K).  2002 Elsevier Science (USA). All rights reserved.