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For the case of a non-commutative base ring R and a right module M < sub > R </ sub > and a left module < sub > R </ sub > N, we can define a bilinear map, where T is an abelian group, such that for any n in N, is a group homomorphism, and for any m in M, is a group homomorphism too, and which also satisfies
Some Related Sentences
For and case
For the case of Jupiter, the radio emission spectrum is definitely not like the spectrum of a black-body radiator, and it seems very likely that the radiation reaching the earth is a combination of thermal radiation from the atmosphere and non-thermal components.
For if such were the case, either the plane of the two lines would meet **zg in more than K points or, alternatively, the order of the image regulus of the pencil determined by the two lines would be too high.
For the case of a purely inertial autonavigator consisting of three restrained gyros, a coordinate system is used where the sensitive axis of the X accelerometer is parallel to the east-west direction at the base point, and the Y accelerometer sensitive axis is parallel to the north-south direction at the base point.
For an ideal gas, the temperature remains constant because the internal energy only depends on temperature in that case.
For private suits only the victims or their families could prosecute, while for public suits anyone ( ho boulomenos, ' whoever wants to ' i. e. any citizen with full citizen rights ) could bring a case since the issues in these major suits were regarded as affecting the community as a whole.
For example a two dimensional array with three rows and four columns might provide access to the element at the 2nd row and 4th column by the expression: ( in a row major language ) and ( in a column major language ) in the case of a zero-based indexing system.
For the frequent case of propositional logic, the problem is decidable but Co-NP-complete, and hence only exponential-time algorithms are believed to exist for general proof tasks.
For the simple case where the direction of the light beam along the line SE is perpendicular to the motion of the observer then only light emitted at an angle equal to the arc cosine of the ratio of the observer's speed to the speed of light will reach the telescope.
For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as its linear momentum,, crossed by its position from the origin, r. Thus, the angular momentum L of a particle with respect to some point of origin is
For larger quantities one must go to a beverage distributor which sells beer only by the case or keg.
For example, bacteria catalyse the breakdown of the mineral pyrite ( FeS < sub > 2 </ sub >) by oxidising the sulfur and metal ( in this case ferrous iron, ( Fe < sup > 2 +</ sup >)) using oxygen.
For case of single stranded DNA / RNA units of nucleotides are used, abbreviated nt ( or knt, Mnt, Gnt ), as they are not paired.
For example in the case of anthrax, it is likely that by 24 – 36 hours after an attack, some small percentage of individuals ( those with compromised immune system or who had received a large dose of the organism due to proximity to the release point ) will become ill with classical symptoms and signs ( including a virtually unique chest X-ray finding, often recognized by public health officials if they receive timely reports ).
For example, most areas of law in most Anglo-American jurisdictions include " statutory law " enacted by a legislature, " regulatory law " promulgated by executive branch agencies pursuant to delegation of rule-making authority from the legislature, and common law or " case law ", i. e., decisions issued by courts ( or quasi-judicial tribunals within agencies ).
For example, civil law can be clearer than case law when the legislature has had the foresight and diligence to address the precise set of facts applicable to a particular situation.
For example, the 1972 Constitution designates the Prime Minister as constitutional successor of the Head of State in case of incapacity, death, resignation or unaccountable absence of the incumbent.
For example, in one case, a prominent Chicana feminist writer and poet has indicated the following subjective meaning through her creative work.
For example in the Netherlands, the law assumes the stronger participant ( e. g. a car driver ) is liable in the case of an accident with a weaker participant ( e. g. a cyclist ) unless it can be proved that the cyclist's behavior could not have been expected.
For and non-commutative
For example, in some groups, the group operation is commutative, and this can be asserted with the introduction of an additional axiom, but without this axiom we can do quite well developing ( the more general ) group theory, and we can even take its negation as an axiom for the study of non-commutative groups.
For square matrices with entries in a non-commutative ring, for instance the quaternions, there is no unique definition for the determinant, and no definition that has all the usual properties of determinants over commutative rings.
For the element A ( t ) from the algebra ( set g with the non-commutative product *), where t is the " time parameter ", the ordered exponential
For the duality between σ-finite measure spaces and commutative von Neumann algebras, noncommutative von Neumann algebras are called non-commutative measure spaces.
For a non-commutative ring, the determinant cannot be defined, but the map GL ( A ) → K < sub > 1 </ sub >( A ) generalizes the determinant.
For and base
For a brief period each year, the rays of the sun are warm enough to melt some of the snows piled a mile deep at the base of the headwalls, and then the pinnacles glisten in the daytime at high noon, and billions of gallons of water begin their slow seepage under the glaciers and across the rockstrewn hanging valleys on their long, meandering journey to the sea -- running east past the sky-carving massifs of Gurla Mandhata and Kemchenjunga, then turning south and curling down through the jungles of Assam, past the Khasi Hills, and into Bengal, past Sirinjani and Madaripur, until the hard water of the melting snows mingles with the soft drainage of fields and at length fans out to meld with the teeming salt depths of the Bay of Bengal.
For the States which maintain two separate agencies -- one for the vocational rehabilitation of the blind, and one for the rehabilitation of persons other than the blind -- the Act specifies that their minimum ( base ) allotment shall be divided between the two agencies in the same proportion as it was divided in fiscal year 1954.
For a vector with linear addressing, the element with index i is located at the address B + c · i, where B is a fixed base address and c a fixed constant, sometimes called the address increment or stride.
For example, if the array has five elements, indexed 1 through 5, and the base address B is replaced by B − 30c, then the indices of those same elements will be 31 to 35.
For a time in the 19th century, stolen bases were credited when a baserunner reached an extra base on a base hit from another player.
For Chrétien, Arthur's chief court was in Caerleon in Wales ; this was the king's primary base in Geoffrey of Monmouth's Historia Regum Britanniae and subsequent literature.
For instance, the largest human chromosome, chromosome number 1, is approximately 220 million base pairs long.
For these reasons, it is often considered a party of the centre-left and its base consists largely of the working class.
For Husserl a sentence has a proposition or judgment as its meaning, and refers to a state of affairs which has a situation of affairs as a reference base.
For elliptic-curve-based protocols, it is assumed that finding the discrete logarithm of a random elliptic curve element with respect to a publicly known base point is infeasible.
For Golb, the amount of documents is too extensive and includes many different writing styles and calligraphies ; the ruins seem to have been a fortress, used as a military base for a very long period of timeincluding the 1st centuryso they could not have been inhabited by the Essenes ; and the large graveyard excavated in 1870, just 50 metres east of the Qumran ruins was made of over 1200 tombs that included many women and childrenPliny clearly wrote that the Essenes that lived near the Dead Sea " had not one woman, had renounced all pleasure ... and no one was born in their race ".
In expert system technology, the knowledge base is expressed with natural language rules IF ... THEN ... For examples:
For instance, 1 / 5 cannot be represented exactly as a floating point number using a binary base but can be represented exactly using a decimal base ( 0. 2, or 2x10 ^- 1 ).
For many years, granite and volcanic rocks have been quarried locally for road base metal, riprap, armour stone and asphalt, although the main purpose now is for concrete aggregates.