Isomorphism Theorem on Vector Spaces over a Ring

Yuichi Futa; Yasunari Shidama

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Displaying similar documents to “Isomorphism Theorem on Vector Spaces over a Ring”

σ-ring and σ-algebra of Sets1

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In this article, semiring and semialgebra of sets are formalized so as to construct a measure of a given set in the next step. Although a semiring of sets has already been formalized in [13], that is, strictly speaking, a definition of a quasi semiring of sets suggested in the last few decades [15]. We adopt a classical definition of a semiring of sets here to avoid such a confusion. Ring of sets and algebra of sets have been formalized as non empty preboolean set [23] and field of subsets...

Moduli space of filtered $λ$ -ring structures over a filtered ring.

Yau, Donald (2004)

International Journal of Mathematics and Mathematical Sciences

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Putcha, Mohan.S., Yaqub, Adil (1979)

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Al-Ezeh, H. (1988)

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Putcha, Mohan S., Yaqub, Adil (1981)

Portugaliae mathematica

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Embedding torsionless modules in projectives.

Carl Faith (1990)

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In this paper we study a condition right FGTF on a ring R, namely when all finitely generated torsionless right R-modules embed in a free module. We show that for a von Neuman regular (VNR) ring R the condition is equivalent to every matrix ring R is a Baer ring; and this is right-left symmetric. Furthermore, for any Utumi VNR, this can be strengthened: R is FGTF iff R is self-injective.

Subrings of I-rings and S-rings.

Sanghare, Mamadou (1997)

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Arens regularity of lattice-ordered rings

Karim Boulabiar, Jamel Jabeur (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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This work discusses the problem of Arens regularity of a lattice-ordered ring. In this prospect, a counterexample is furnished to show that without extra conditions, a lattice-ordered ring need not be Arens regular. However, as shown in this paper, it turns out that any $f$ -ring in the sense of Birkhoff and Pierce is Arens regular. This result is then used and extended to the more general setting of almost $f$ -rings introduced again by Birkhoff.