Unitization of Ball truncated $${\ell}$$ ℓ -groups

Unitization of Ball truncated $${\ell}$$ ℓ -groups Recently, Ball defined a truncated $${\ell}$$ ℓ -group to be an $${\ell}$$ ℓ -group G along with a truncation. We constructively prove that if G is a truncated $${\ell}$$ ℓ -group, then the direct sum $${G \oplus \mathbb{Q}}$$ G ⊕ Q is equipped with a structure of an $${\ell}$$ ℓ -group with weak unit the rational number 1. As a simple consequence, we get a description of the truncated $${\ell}$$ ℓ - group obtained by Ball via representation theory. On the other hand, we derive some characterizations of truncation morphisms as defined by Ball himself. In particular, we show that the group homomorphism $${f : G \rightarrow H}$$ f : G → H is a truncation morphism if and only its natural extension $${f^*}$$ f ∗ from $${G \oplus \mathbb{Q}}$$ G ⊕ Q into $${H \oplus \mathbb{Q}}$$ H ⊕ Q is an $${\ell}$$ ℓ -homomorphism. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png algebra universalis Springer Journals

Unitization of Ball truncated $${\ell}$$ ℓ -groups

Loading next page...
 
/lp/springer_journal/unitization-of-ball-truncated-ell-groups-bKmb9GnWii
Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing
Subject
Mathematics; Algebra
ISSN
0002-5240
eISSN
1420-8911
D.O.I.
10.1007/s00012-017-0444-1
Publisher site
See Article on Publisher Site

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial