# The Borromean Rings

## Related Articles

- Book reviews. Kaplansky, Irving // Bulletin (New Series) of the American Mathematical Society;Jul1994, Vol. 31 Issue 1, p146
Reviews the book, `Topological rings,' by Seth Warner.

- Topological Properties of Inverse Limits of Free Abelian Monoids, with an Application to Inverse Limits of UFDs. Snellman, Jan // Semigroup Forum;1999, Vol. 59 Issue 3, p418
Discusses topological properties of inverse limits of free abelian monoids. Multiplicative monoids of topological rings; Inverse limits of topological monoids.

- unit theory. // Hutchinson Dictionary of Scientific Biography;2005, p1
In a field or ring, involves an element that possesses an inverse. In a field, every nonzero element is a unit; in a ring, 1 and -1 represent a unit.

- The Topological Nearring on the Euclidean Plane Which Has a Left Identity Which is Not a Right Identity. Magill Jr., K.D. // Semigroup Forum;1998, Vol. 57 Issue 3, p435
Presents a study that analyzed the topological nearring on the Euclidian plane which has a left identity. Background on a topological nearring; Formulation of the main theorem; Results and discussion.

- New formation of topological matter of NbSe3. Tanda, S.; Tsuneta, T.; Okajima, Y.; Yamaya, K. // AIP Conference Proceedings;2001, Vol. 591 Issue 1, p473
We have synthesized new topological ring-shaped and figure-8 crystals of NbSe[sub3] grown from chemical vapor transportation. We confirm that the ring-NbSe[sub3] is a single-phase crystal from X-ray diffraction, and that a charge-density wave (CDW) transition takes place near 140 K by observing...

- On Unions of Prime Submodules. Çallıalp, Fethi; Tekir, Ünsal // Southeast Asian Bulletin of Mathematics;2004, Vol. 28 Issue 2, p213
Let R be a commutative ring and M be an R-module. A proper submodule N of M is said to be prime if rm âˆˆ N for r âˆˆ R and m âˆˆ M implies that either m âˆˆ N or r âˆˆ (N : M). In this paper, we investigate finite and infinite unions of submodules of R-module M.

- A topological prime quasi-radical. Bazigaran, B.; Glavatsky, S.; Mikhalev, A. // Journal of Mathematical Sciences;Dec2006, Vol. 139 Issue 4, p6663
In this paper, we consider a topological prime quasi-radical Î¼( R), which is the intersection of closed prime ideals in a topological ring R. Examples are given that show that Î¼( R) is different from those topological analogs of the prime radical that have been studied earlier. The...

- TOTALLY BOUNDED ENDOMORPHISMS ON A TOPOLOGICAL RING. Mirzavaziri, Madjid; Zabeti, Omid // Matematicki Vesnik;2013, Vol. 65 Issue 3, p419
Let X be a topological ring. In this paper, we consider the three classes (btb-bounded, tbtb-bounded, and tbb-bounded) of endomorphisms defined on X and denote these classes by Bbtb(X), Btbtb(X), and Btbb(X), respectively. We equip them with an appropriate topology and we find some sufficient...

- Characterizations of regular hyperrings by prime and semi-prime hyperideals. Velrajan, M.; Asokkumar, A. // Journal of Advanced Research in Pure Mathematics;2012, Vol. 4 Issue 2, p88
In this paper, we give two characterizations of regular hyperrings. We prove that a commutative hyperring R with an identity is regular if and only if every hyperideal in R; maximal with respect to the property of not having a given element in R; is a prime hyperideal. The other characterization...