In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R. Thus A is endowed with binary operations of addition and multiplication satisfying a number of axioms, including associativity of multiplication and distributivity, as well as compatible multiplication by the elements of the field K or the ring R.

In addition to the ECS module, 1982 also saw the introduction of a redesigned model, called the Intellivision II ( featuring detachable controllers and sleeker case ), the System Changer ( which played Atari 2600 games on the Intellivision II ), and a music keyboard add-on for the ECS.

In mathematics, a linear map, linear mapping, linear transformation, or linear operator ( in some contexts also called linear function ) is a function between two modules ( including vector spaces ) that preserves the operations of module ( or vector ) addition and scalar multiplication.

In addition to the laboratory module, the complete set also included five external pallets for experiments in vacuum, built by British Aerospace ( BAe ) and a pressurized igloo containing the subsystems needed for the pallet-only flight configuration operation.

As a ring, its addition law is that of the free module and its multiplication extends " by linearity " the given group law on the basis.

* For every index set I, the addition map M < sup >( I )</ sup > → M can be extended to a module homomorphism M < sup > I </ sup > → M ( here M < sup >( I )</ sup > denotes the direct sum of copies of M, one for each element of I ; M < sup > I </ sup > denotes the product of copies of M, one for each element of I ).

Pioneer Electronics ( USA ) and Sega Enterprises released this module that allows users to play 8-inch and 12-inch LaserActive Mega LD discs, in addition to the hundreds of existing SEGA-CD and Genesis titles, as well as standard CD + G discs.

In addition, the ship possesses an aft torpedo launcher and is capable of firing a powerful disruptor beam from the forward module.

Telebit first offered V. 32 support in the T2500, which used the Trailblazer / T2000 hardware with the addition of the Rockwell V. 32 modem module.

In addition, they installed three materials experiments, called SKK for their Russian acronym, on the Zvezda module.

The internal architecture prohibited the addition of more memory, so HP designed an extended memory module that could be seen as secondary storage.

RKK Energia, the manufacturer of the ROS components, proposes to execute a similar to the original ISS plan with the addition of a Nodal module and two additional science / energy modules to the segment around 2013-2015.

The EX module code stands for extension, as the adventure is designed to be inserted as an independent addition to another, ongoing scenario.

In addition to connecting to the Zarya module, Unity currently connects to the U. S. Destiny Laboratory Module ( added on STS-98 ), the Z1 truss ( an early exterior framework for the station added on STS-92 ), the PMA-3 ( also added on STS-92 ), and the Quest Joint Airlock ( added on STS-104 ).

In addition to the tamper-evident physical security mechanisms required at Security Level 2, Security Level 3 attempts to prevent the intruder from gaining access to CSPs held within the cryptographic module.

In addition, one of the flights, STS-74, carried new components to Mir, consisting of a docking module and a pair solar arrays.

The module presented so far NAT which represented the natural numbers and addition on its elements, is considered a functional module / rewrite theory, since it contains no rewrite rules.

* Engineering Division USD-9A, a modified Airco DH. 9A ( 1921-the first aircraft to fly with the addition of a pressurized cockpit module )

For example, in addition to the drug module for the popular medical dispensaries ( which provided free access to 106 essential medicines designed to cover the needs at this level of care ), a family drug module was launched in 2005.

In mathematics, a topological module is a module over a topological ring such that scalar multiplication and addition are continuous.

Beside the fuel injection, a significant change for the Z24i was the addition of an optical crank angle sensor in the distributor rather than a vacuum advance and ignition module.

In addition, our way of dealing directly with natural phenomena has also changed.

Besides showing no inclination, apparently, to absent himself from his native region even for short periods, and in addition writing a shelf of books set in the region, he has handled in those books an astonishingly complete list of matters which have been important in the South during the past hundred years.

In San Francisco he has worked with Brew Moore, Charlie Mingus, and other `` swinging '' musicians of secure reputation, thus placing himself within established jazz traditions, in addition to being a part of the San Francisco `` School ''.

In addition, he said, he has answered more than 400 messages of congratulations which led him to the comment that he himself had decided he wouldn't send another congratulatory message for the rest of his life.

In addition, the motor has the seal of approval of the Underwriters Laboratories, which means it is safe.

Thus, there has come into being a situation in which the state must raise all of its own revenues and, in addition, must give assistance to its local governments.

In addition to the basic programs in wavelength standards, spectroscopy, solid state physics, interactions of the free electron and atomic constants which are necessary to provide the foundation for technological progress, the Bureau has strengthened its activities in laboratory astrophysics.

In addition, petitioner has failed to show any particular need for the report and notes.

In addition, land has been purchased to permit doubling the size of the plant in the future.

In addition to these rules, Carleton has added the following: 1.

In addition, little work has been done on a comparative basis in regard to the normal existence of bronchial artery-pulmonary artery anastomoses.

In addition, this country has been settled by many peoples of many heritages and their lore has become acculturated slowly, in an age of print and easy communication, within an ever-expanding and changing society.

In addition, Dr. Clark has studied at Rhode Island State College and Massachusetts Institute of Technology.

In addition to the interlibrary loan service and the children's program, headquarters has a public relations director who seeks to get wider grassroots support for quality library service in the county ; ;

For this latest addition to the Great Letters Series, under the general editorship of Louis Kronenberger, Miss Hardwick has made a selection which admirably displays the variety of James's genius, not to mention the felicities of his style.

In addition, mixed race ( European and African ) people amount to about 2 %, with a small ( 1 %) population of whites, mainly ethnically Portuguese ( as a former overseas territory of Portugal until 1975, the Portuguese make up currently the largest non-African population, with certainly more than 100, 000, a number that has been constantly increasing from the 2000s, because of Angola's growing demand for qualified human resources.

Roughly 26 % are followers of traditional forms of Protestantism ( Congregationals, Methodists, Baptista, Lutherans, Reformed ), but over the last decades there has in addition been a growth of Pentecostal communities and African Initiated Churches.

As per the American Dental Association, regular brushing and proper flossing are enough in most cases although the ADA has placed its Seal of Approval on many mouthwashes containing alcohol ( in addition to regular dental check-ups ).

Since then commercial interest in mouthwashes has been intense and several newer products claim effectiveness in reducing the build-up in dental plaque and the associated severity of gingivitis ( inflammation of the gums ), in addition to fighting bad breath.

In addition to the Conservatory, AFI has a tuition-free program called the AFI Directing Workshop for Women that operates each spring and summer from the Los Angeles campus.

Conium maculatum has been used as a sedative and in treatments for arthritis and asthma in addition to its most famous use: as a “ humane ” method of killing criminals and philosophers.

* In elementary arithmetic, the set of integers, Z, considered as a group under addition, has a unique nontrivial automorphism: negation.

In addition, Sirius has been played in a variety of TV shows and movies including the episode " Vanishing Act " of The Adventures of Jimmy Neutron: Boy Genius, and the 2009 film Cloudy with a Chance of Meatballs.

Xylenol has two methyl groups in addition to the hydroxyl group, and, for this structure, 6 isomers exist.