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 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 this module has many of the tools required for controlling different 3D views and user coordinate systems.

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 the latter half of the 20th century, the influence of the romance tradition of Arthur continued, through novels such as T. H. White's The Once and Future King ( 1958 ) and Marion Zimmer Bradley's The Mists of Avalon ( 1982 ) in addition to comic strips such as Prince Valiant ( from 1937 onward ).

In addition, Nickelodeon had removed the half-hour edits of the 1981 episodes of You Can't Do That on Television from its daily time slot rotation, along with the 1982 " Cosmetics " episode.

In addition to the career steals record, Henderson also holds the single-season record for stolen bases ( 130 in 1982 ) and is the only player in AL history to steal 100 bases in a season, having done so three times.

In addition to the many impressed critics, President Ronald Reagan and first lady Nancy Reagan were moved by the film after a screening at the White House on June 27, 1982.

In addition, BS12 was ahead of SQL in supporting user-defined functions and procedures, using a computationally complete sublanguage, triggers, and a simple " call " interface for use by application programs, all in its very first release in 1982.

While colours and detail specifications were modified in the ensuing 42 years, the biggest mechanical change was the addition of front disc brakes in 1981 ( from the discontinued Citroën Dyane ), for the 1982 model year.

The Constitution Act, 1982, greatly expanded the role of the court in Canadian society by the addition of the Canadian Charter of Rights and Freedoms, which greatly broadened the scope of judicial review.

In addition to diesel buses, Nancy has been served by trolleybuses since 1982, but in 2000 the three-route trolleybus system was reconfigured into a single, longer route and with a surface guidance system added ( GLT, or TVR in French ).

With the addition of new bass player, Giorgio Kilkenny, this line-up recorded Too-Rye-Ay in 1982, a hybrid of soul and Celtic folk, the new sound accompanied by a new fabulous look, with the band attired in dungarees, scarves, leather waistcoats, and what was described as " a generally scruffy right-off-the-farm look ", or " a raggle-taggle mixture of gypsy, rural Irish and Steinbeck Okie ".

In addition, the 1982 Constitution provides an extensive legal framework for the liberalizing economic policies of the 1980s.

In addition, the 1982 document reflects the more flexible and less ideological orientation of foreign policy since 1978.

Changes involved an addition to the title — as opposed to a number attached to the end — like " The Final Chapter " and " Jason Takes Manhattan ", or filming the movie in 3-D, as Miner did for Friday the 13th Part III ( 1982 ).

The book has been reprinted many times: in 1953 by Galaxy, in 1957 and 1964 by Bantam, in 1958 and 1982 by Corgi as the first British edition, in 1968 by Sidgwick & Jackson in hardcover, in 1969, 1972, 1974 ( both paper and hard cover editions ) and 1981 by Sphere Science Fiction, in 1971 and 1975 by Fawcett Books, in 1983 by Del Ray Books, in 1986 in hardcover by Grafton and in 1990 again by Doubleday in hardcover ; in addition, it was reprinted as part of the Empire series, in 1986 by Ballantine Books, in 1992 by Spectra and in 2010 by Orb Books, in both print and Kindle editions.

" Prologue " is a late addition to the show, not included in any recordings produced before the 1982 Broadway production ; the use of " Any Dream Will Do " at the start of the show ( and the renaming of the closing version as per the above list ) dates from the 1991 revival.

In addition to Thames ' departure from the network as franchise owners, it could also be argued that an equally significant part of the changeover was the fact that its replacement, Carlton Communications, broke away from the traditions of the 1968 and 1982 franchise rounds, in not acquiring and taking-over the bulk of its predecessors ' studios, facilities, work-force and infrastructure.

In addition to The Jewel in the Crown, this cycle also included Gandhi ( 1982 ), Heat and Dust ( 1983 ), The Far Pavilions ( 1984 ) and A Passage to India ( 1984 ).

* In addition, guest appearances in more than a dozen television shows ( 1982 – present )

In addition, he is also remembered for his roles as Luther Billis in South Pacific ( 1949 / 1958 ), Mr. Applegate in Damn Yankees ( 1955 / 1958 ), J. J. Singleton in The Sting ( 1973 ), high school teacher Mr. Hand in Fast Times at Ridgemont High ( 1982 ), and Judge Henry Bone on the drama series Picket Fences ( 1992-1996 ).

In addition to the Soyuz and Progress spacecraft, after the final crew had left, Salyut 6 was visited by an experimental transport logistics spacecraft called Kosmos 1267 in 1982.

In addition to The Odd Couple, The Mary Tyler Moore Show and Happy Days, other live sitcoms that were sweetened by Douglass were The Paul Lynde Show ( ABC, 1972 – 73 ), The Bob Newhart Show ( CBS, 1972 – 78 ), Maude ( CBS, 1972 – 78 ), Rhoda ( CBS, 1974 – 78 ), Laverne and Shirley ( ABC, 1976 – 83 ), Alice ( CBS, 1976 – 85 ), Soap ( ABC, 1977 – 81 ), Taxi ( ABC, 1978 – 82 ; NBC, 1982 – 83 ), Seinfeld ( NBC 1990-1998 ), Friends ( NBC 1994-2004 ), Cheers ( NBC, 1982 – 93 ) and its spinoff Frasier ( NBC, 1993 – 2004 ).

It song list and order sticks very closely to the 1982 Song and Dance version, with the addition of the finale song " Dreams Never Run On Time ", itself a rewrite of the song from the 2003 version " Somewhere, Someplace, Sometime ".

Visage, now without Ure, McGeoch and Adamson ( who continued collaborating with Pete Shelley, and joined Nick Cave and the Bad Seeds ) but now with the addition of bassist Steve Barnacle, recorded the stand-alone single " Pleasure Boys ", which was released in October 1982.

In addition, he was the " National Motorsports Press Association Driver of the Year ", ( 1977, 1981, 1982 ), the " Auto Racing Digest Driver of the Year ", ( 1981, 1982 ) and the first " Tennessee Professional Athlete of the Year ", ( 1979 ).