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Almost smooth algebras

Alfredo R. Grandjean, Maria J. Vale (1991)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Essential Cover and Closure

Andruszkiewicz, R. (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 16N80, 16S70, 16D25, 13G05.We construct some new examples showing that Heyman and Roos construction of the essential closure in the class of associative rings can terminate at any finite or the first infinite ordinal.

Nil-extensions of completely simple semirings

Sunil K. Maity, Rituparna Ghosh (2013)

Discussiones Mathematicae - General Algebra and Applications

A semiring S is said to be a quasi completely regular semiring if for any a ∈ S there exists a positive integer n such that na is completely regular. The present paper is devoted to the study of completely Archimedean semirings. We show that a semiring S is a completely Archimedean semiring if and only if it is a nil-extension of a completely simple semiring. This result extends the crucial structure theorem of completely Archimedean semigroup.

Relationship of certain rings of infinite matrices over integers

Mario Petrich, Pedro V. Silva (2000)

Bollettino dell'Unione Matematica Italiana

Sia N l'insieme degli interi non negativi e Z l'anello degli interi. Sia A l'anello delle matrici N × N su Z che hanno solo un numero finito di cifre non nulle in ogni linea ed in ogni colonna. Sia B il sottoanello generato da X e Y , dove X (rispettivamente Y ) è ottenuto dalla matrice identità muovendo gli 1 una posizione a destra (rispettivamente in giù). Sia pure C il sottoanello di A generato da 1 - X e 1 - Y . Infine sia F il sottoanello delle matrici di A che hanno solo un numero finito di cifre non nulle....

Split-null extensions of strongly right bounded rings.

Gary F. Birkenmeier (1990)

Publicacions Matemàtiques

A ring is said to be strongly right bounded if every nonzero right ideal contains a nonzero ideal. In this paper strongly right bounded rings are characterized, conditions are determined which ensure that the split-null (or trivial) extension of a ring is strongly right bounded, and we characterize strongly right bounded right quasi-continuous split-null extensions of a left faithful ideal over a semiprime ring. This last result partially generalizes a result of C. Faith concerning split-null extensions...

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