Simple (abstract algebra)

In mathematics, the term simple is used to describe an algebraic structure which in some sense cannot be divided by a smaller structure of the same type. Put another way, an algebraic structure is simple if the kernel of every homomorphism is either the whole structure or a single element. Some examples are:

  • A group is called a simple group if it does not contain a nontrivial proper normal subgroup.
  • A ring is called a simple ring if it does not contain a nontrivial two sided ideal.
  • A module is called a simple module if it does not contain a nontrivial submodule.
  • An algebra is called a simple algebra if it does not contain a nontrivial two sided ideal.
  • The general pattern is that the structure admits no non-trivial congruence relations.

    The term is used differently in semigroup theory. A semigroup is said to be simple if it has no nontrivial ideals, or equivalently, if Green's relation J is the universal relation. Not every congruence on a semigroup is associated with an ideal, so a simple semigroup may have nontrivial congruences. A semigroup with no nontrivial congruences is called congruence simple.

    Passion (Kreesha Turner album)

    Passion is the first album by the Canadian singer Kreesha Turner. It was released on August 12, 2008, in Canada and was released in early 2009 in the United States.Passion had been available for advanced streaming on MuchMusic.com. a week earlier.Passion was released in the US in early 2009.

    In early August, 2008, the album was leaked onto MTV Canada's The Leak on its official website.

    Initially, on the back of the album, track 14 was listed as the "Bounce With Me (Rhythm Mix)" but this was an error and the track is actually the "Don't Call Me Baby (Rhythm Mix)". This error on the back cover was corrected on later pressings of the album.

    Although Turner originally signed in the US to Virgin Records, a Capitol Music Group label, her first American release will instead be shifted to the Capitol Records imprint, also within the Capitol Music Group umbrella. This will keep a consistency with her Canadian releases under EMI Music Canada which utilize the Capitol Records imprint and are copyrighted by Capitol Records, LLC.

    Simple (bank)

    Simple is an American direct bank based in Portland, Oregon. The company provides FDIC-insured checking accounts through a partnership with The Bancorp and is part of the STAR network for surcharge-free access to around 55,000 ATMs. Since 2014, Simple has been part of the BBVA Group, one of the largest banks in Europe.

    History

    What was initially known as BankSimple was founded in 2009 in Brooklyn by former CTO Alex Payne, CEO Joshua Reich and CFO Shamir Karkal. In August 2011, the company raised $10 million from investors led by IA Ventures, Shasta Ventures and Dave McClure's fund 500 Startups. Later that month, the company moved its headquarters to Portland, where five of the company's 17 employees already resided.

    The company launched in the summer of 2012 as a limited beta.

    By January 2013, the company had 20,000 customers and had processed more than $200 million in transactions. By July 2013, its customers had increased to 40,000 and total transaction values increased to greater than $1 billion. At year's end in 2013, Simple reported processing on average around 13 debit transactions per minute with an overall customer balance of $64 million.

    Ion

    An ion (/ˈən, -ɒn/) is an atom or a molecule in which the total number of electrons is not equal to the total number of protons, giving the atom or molecule a net positive or negative electrical charge. Ions can be created, by either chemical or physical means, via ionization.

    In chemical terms, if a neutral atom loses one or more electrons, it has a net positive charge and is known as a cation.

    If an atom gains electrons, it has a net negative charge and is known as an anion.

    An ion consisting of a single atom is an atomic or monatomic ion; if it consists of two or more atoms, it is a molecular or polyatomic ion. Because of their electric charges, cations and anions attract each other and readily form ionic compounds, such as salts.

    In the case of physical ionization of a medium, such as a gas, what are known as "ion pairs" are created by ion impact, and each pair consists of a free electron and a positive ion.

    History of discovery

    The word ion is the Greek ἰόν, ion, "going", the present participle of ἰέναι, ienai, "to go". This term was introduced by English physicist and chemist Michael Faraday in 1834 for the then-unknown species that goes from one electrode to the other through an aqueous medium. Faraday did not know the nature of these species, but he knew that since metals dissolved into and entered a solution at one electrode, and new metal came forth from a solution at the other electrode, that some kind of substance moved through the solution in a current, conveying matter from one place to the other.

    Ion (DC Comics)

    Ion is a fictional character, a DC Comics superhero. Created by writer Judd Winick and artist Dale Eaglesham for Green Lantern vol. 3 #142, Ion was devised as the new superhero identity for Green Lantern protagonist Kyle Rayner. It was later revealed to be able to form mutualism with a host, bestowing its power to a host willingly. This followed a similar retcon as Parallax, originally the new supervillain alias of Hal Jordan, which was revealed to be a parasitic embodiment of fear in the 2004–2005 miniseries Green Lantern: Rebirth.

    Fictional character biography

    As soon as sentient beings developed willpower, Ion was born from the green wavelength of the so-called "emotional spectrum". Its existence has been kept a secret for eons, and it resided in the Central Battery on Oa to keep Parallax, the parasitic fear entity also imprisoned there, in check, as well as granting the Guardians of the Universe, Manhunters, The Green Glob, Halla's, and then The Green Lantern Corps a portion of its vast powers. After Hal Jordan, under the influences of Parallax and Sinestro, destroyed the Central Battery, Ion, along with Parallax and Sinestro, were set free. After wandering throughout the cosmos, it eventually settled within Kyle Rayner as its host.

    Ion (name)

    Ion is a masculine given name. The name form in English corresponds to two different and unrelated names from different original languages.

    The first name is the Greek,Ἴων, Iōn, after the mythical founder of the Ionians; the modern (demotic) Greek equivalent of the name is Ionas. The source of this is the Hebrew Yavan, alternatively transliterated as ι-o-ν (Yut Vav/digamma Nun), with each letter corresponding to its appropriate counterpart.

    The second name is the Romanian Ion which is equivalent to the English name John and has the same etymology as "Jon", tracing back the Hebrew name Johanan; Ion can also be a surname in Romanian. Another variant is Ioan. A common diminutive is Ionel. Its female form is Ioana. The surname Ionescu derives from Ion.

    Ion as a given name

  • Ion (mythology)
  • Ion of Chios (c. 490/480-c. 420 BC), Greek writer, dramatist, lyric poet and philosopher
  • Ion, a professional rhapsode of the platonic dialogue of the same name
  • Ion Dragoumis (1878–1920), Greek diplomat, philosopher, writer and revolutionary
  • Podcasts:

    developed with YouTube
    PLAYLIST TIME:

    Cymbaline

    by: Pink Floyd

    The path you tread is narrow
    And the drop is shear and very high
    The ravens all are watching
    From a vantage point nearby
    Apprehension creeping
    Like a tube-train up your spine
    Will the tightrope reach the end
    Will the final couplet rhyme
    And it's high time, Cymbaline
    It is high time, Cymbaline
    Please wake me
    A butterfly with broken wings
    Is falling by your side
    The ravens all are closing in
    There's nowhere you can hide
    Your manager and agent
    Are both busy on the phone
    Selling colored photographs
    To magazines back home
    And it's high time, Cymbaline
    It is high time, Cymbaline
    Please wake me
    The lines converging where you stand
    They must have moved the picture plane
    The leaves are heavy around your feet
    You hear the thunder of the train
    And suddenly it strikes you
    That they're moving into range
    And Doctor Strange
    Is always changing size
    And it's high time, Cymbaline
    It is high time, Cymbaline
    Please wake me
    And it's high time, Cymbaline
    It is high time, Cymbaline




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